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| linear algebra and matrix theory: Linear Algebra and Matrix Theory Jimmie Gilbert, Linda Gilbert, 2014-06-28 Intended for a serious first course or a second course, this textbook will carry students beyond eigenvalues and eigenvectors to the classification of bilinear forms, to normal matrices, to spectral decompositions, and to the Jordan form. The authors approach their subject in a comprehensive and accessible manner, presenting notation and terminology clearly and concisely, and providing smooth transitions between topics. The examples and exercises are well designed and will aid diligent students in understanding both computational and theoretical aspects. In all, the straightest, smoothest path to the heart of linear algebra.* Special Features: * Provides complete coverage of central material.* Presents clear and direct explanations.* Includes classroom tested material.* Bridges the gap from lower division to upper division work.* Allows instructors alternatives for introductory or second-level courses. |
| linear algebra and matrix theory: Linear Algebra and Matrix Theory Robert R. Stoll, 2012-10-17 Advanced undergraduate and first-year graduate students have long regarded this text as one of the best available works on matrix theory in the context of modern algebra. Teachers and students will find it particularly suited to bridging the gap between ordinary undergraduate mathematics and completely abstract mathematics. The first five chapters treat topics important to economics, psychology, statistics, physics, and mathematics. Subjects include equivalence relations for matrixes, postulational approaches to determinants, and bilinear, quadratic, and Hermitian forms in their natural settings. The final chapters apply chiefly to students of engineering, physics, and advanced mathematics. They explore groups and rings, canonical forms for matrixes with respect to similarity via representations of linear transformations, and unitary and Euclidean vector spaces. Numerous examples appear throughout the text. |
| linear algebra and matrix theory: Matrix Theory: A Second Course James M. Ortega, 2013-11-11 Linear algebra and matrix theory are essentially synonymous terms for an area of mathematics that has become one of the most useful and pervasive tools in a wide range of disciplines. It is also a subject of great mathematical beauty. In consequence of both of these facts, linear algebra has increasingly been brought into lower levels of the curriculum, either in conjunction with the calculus or separate from it but at the same level. A large and still growing number of textbooks has been written to satisfy this need, aimed at students at the junior, sophomore, or even freshman levels. Thus, most students now obtaining a bachelor's degree in the sciences or engineering have had some exposure to linear algebra. But rarely, even when solid courses are taken at the junior or senior levels, do these students have an adequate working knowledge of the subject to be useful in graduate work or in research and development activities in government and industry. In particular, most elementary courses stop at the point of canonical forms, so that while the student may have seen the Jordan and other canonical forms, there is usually little appreciation of their usefulness. And there is almost never time in the elementary courses to deal with more specialized topics like nonnegative matrices, inertia theorems, and so on. In consequence, many graduate courses in mathematics, applied mathe matics, or applications develop certain parts of matrix theory as needed. |
| linear algebra and matrix theory: Linear Algebra and Matrix Theory Evar D. Nering, 1970 |
| linear algebra and matrix theory: Matrix Theory Fuzhen Zhang, 2013-03-14 This volume concisely presents fundamental ideas, results, and techniques in linear algebra and mainly matrix theory. Each chapter focuses on the results, techniques, and methods that are beautiful, interesting, and representative, followed by carefully selected problems. For many theorems several different proofs are given. The only prerequisites are a decent background in elementary linear algebra and calculus. |
| linear algebra and matrix theory: Linear Algebra: Theory and Applications Kenneth Kuttler, 2012-01-29 This is a book on linear algebra and matrix theory. While it is self contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed that the reader has had calculus. Some optional topics require more analysis than this, however. I think that the subject of linear algebra is likely the most significant topic discussed in undergraduate mathematics courses. Part of the reason for this is its usefulness in unifying so many different topics. Linear algebra is essential in analysis, applied math, and even in theoretical mathematics. This is the point of view of this book, more than a presentation of linear algebra for its own sake. This is why there are numerous applications, some fairly unusual. |
| linear algebra and matrix theory: Linear Algebra and Matrix Analysis for Statistics Sudipto Banerjee, Anindya Roy, 2014-06-06 Linear Algebra and Matrix Analysis for Statistics offers a gradual exposition to linear algebra without sacrificing the rigor of the subject. It presents both the vector space approach and the canonical forms in matrix theory. The book is as self-contained as possible, assuming no prior knowledge of linear algebra. The authors first address the rudimentary mechanics of linear systems using Gaussian elimination and the resulting decompositions. They introduce Euclidean vector spaces using less abstract concepts and make connections to systems of linear equations wherever possible. After illustrating the importance of the rank of a matrix, they discuss complementary subspaces, oblique projectors, orthogonality, orthogonal projections and projectors, and orthogonal reduction. The text then shows how the theoretical concepts developed are handy in analyzing solutions for linear systems. The authors also explain how determinants are useful for characterizing and deriving properties concerning matrices and linear systems. They then cover eigenvalues, eigenvectors, singular value decomposition, Jordan decomposition (including a proof), quadratic forms, and Kronecker and Hadamard products. The book concludes with accessible treatments of advanced topics, such as linear iterative systems, convergence of matrices, more general vector spaces, linear transformations, and Hilbert spaces. |
| linear algebra and matrix theory: The Mathematics of Matrices Philip J. Davis, 1973 |
| linear algebra and matrix theory: Introduction to Modern Algebra and Matrix Theory Otto Schreier, Emanuel Sperner, 2011-01-01 This unique text provides students with a basic course in both calculus and analytic geometry. It promotes an intuitive approach to calculus and emphasizes algebraic concepts. Minimal prerequisites. Numerous exercises. 1951 edition-- |
| linear algebra and matrix theory: Problems In Linear Algebra And Matrix Theory Fuzhen Zhang, 2021-10-25 This is the revised and expanded edition of the problem book Linear Algebra: Challenging Problems for Students, now entitled Problems in Linear Algebra and Matrix Theory. This new edition contains about fifty-five examples and many new problems, based on the author's lecture notes of Advanced Linear Algebra classes at Nova Southeastern University (NSU-Florida) and short lectures Matrix Gems at Shanghai University and Beijing Normal University.The book is intended for upper division undergraduate and beginning graduate students, and it can be used as text or supplement for a second course in linear algebra. Each chapter starts with Definitions, Facts, and Examples, followed by problems. Hints and solutions to all problems are also provided. |
| linear algebra and matrix theory: Finite-Dimensional Vector Spaces Paul R. Halmos, 2017-05-24 Classic, widely cited, and accessible treatment offers an ideal supplement to many traditional linear algebra texts. Extremely well-written and logical, with short and elegant proofs. — MAA Reviews. 1958 edition. |
| linear algebra and matrix theory: Introduction to Linear and Matrix Algebra Nathaniel Johnston, 2021-05-19 This textbook emphasizes the interplay between algebra and geometry to motivate the study of linear algebra. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. By focusing on this interface, the author offers a conceptual appreciation of the mathematics that is at the heart of further theory and applications. Those continuing to a second course in linear algebra will appreciate the companion volume Advanced Linear and Matrix Algebra. Starting with an introduction to vectors, matrices, and linear transformations, the book focuses on building a geometric intuition of what these tools represent. Linear systems offer a powerful application of the ideas seen so far, and lead onto the introduction of subspaces, linear independence, bases, and rank. Investigation then focuses on the algebraic properties of matrices that illuminate the geometry of the linear transformations that they represent. Determinants, eigenvalues, and eigenvectors all benefit from this geometric viewpoint. Throughout, “Extra Topic” sections augment the core content with a wide range of ideas and applications, from linear programming, to power iteration and linear recurrence relations. Exercises of all levels accompany each section, including many designed to be tackled using computer software. Introduction to Linear and Matrix Algebra is ideal for an introductory proof-based linear algebra course. The engaging color presentation and frequent marginal notes showcase the author’s visual approach. Students are assumed to have completed one or two university-level mathematics courses, though calculus is not an explicit requirement. Instructors will appreciate the ample opportunities to choose topics that align with the needs of each classroom, and the online homework sets that are available through WeBWorK. |
| linear algebra and matrix theory: Matrix Theory and Linear Algebra Israel N. Herstein, David J. Winter, 1989 |
| linear algebra and matrix theory: A Second Course in Linear Algebra Stephan Ramon Garcia, Roger A. Horn, 2017-05-11 A second course in linear algebra for undergraduates in mathematics, computer science, physics, statistics, and the biological sciences. |
| linear algebra and matrix theory: Linear Algebra and Matrix Theory Robert R. Stoll, 2013-05-20 One of the best available works on matrix theory in the context of modern algebra, this text bridges the gap between ordinary undergraduate studies and completely abstract mathematics. 1952 edition. |
| linear algebra and matrix theory: Matrix Algebra James E. Gentle, 2007-07-27 Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. |
| linear algebra and matrix theory: Linear Algebra and Matrices Shmuel Friedland, Mohsen Aliabadi, 2018-01-30 This introductory textbook grew out of several courses in linear algebra given over more than a decade and includes such helpful material as constructive discussions about the motivation of fundamental concepts, many worked-out problems in each chapter, and topics rarely covered in typical linear algebra textbooks.The authors use abstract notions and arguments to give the complete proof of the Jordan canonical form and, more generally, the rational canonical form of square matrices over fields. They also provide the notion of tensor products of vector spaces and linear transformations. Matrices are treated in depth, with coverage of the stability of matrix iterations, the eigenvalue properties of linear transformations in inner product spaces, singular value decomposition, and min-max characterizations of Hermitian matrices and nonnegative irreducible matrices. The authors show the many topics and tools encompassed by modern linear algebra to emphasize its relationship to other areas of mathematics. The text is intended for advanced undergraduate students. Beginning graduate students seeking an introduction to the subject will also find it of interest. |
| linear algebra and matrix theory: Elements of Linear Algebra and Matrix Theory John T. Moore, 1968 |
| linear algebra and matrix theory: Matrix Analysis and Applied Linear Algebra Carl D. Meyer, 2000-06-01 This book avoids the traditional definition-theorem-proof format; instead a fresh approach introduces a variety of problems and examples all in a clear and informal style. The in-depth focus on applications separates this book from others, and helps students to see how linear algebra can be applied to real-life situations. Some of the more contemporary topics of applied linear algebra are included here which are not normally found in undergraduate textbooks. Theoretical developments are always accompanied with detailed examples, and each section ends with a number of exercises from which students can gain further insight. Moreover, the inclusion of historical information provides personal insights into the mathematicians who developed this subject. The textbook contains numerous examples and exercises, historical notes, and comments on numerical performance and the possible pitfalls of algorithms. Solutions to all of the exercises are provided, as well as a CD-ROM containing a searchable copy of the textbook. |
| linear algebra and matrix theory: Linear Algebra and Matrices Helene Shapiro, 2015-10-08 Linear algebra and matrix theory are fundamental tools for almost every area of mathematics, both pure and applied. This book combines coverage of core topics with an introduction to some areas in which linear algebra plays a key role, for example, block designs, directed graphs, error correcting codes, and linear dynamical systems. Notable features include a discussion of the Weyr characteristic and Weyr canonical forms, and their relationship to the better-known Jordan canonical form; the use of block cyclic matrices and directed graphs to prove Frobenius's theorem on the structure of the eigenvalues of a nonnegative, irreducible matrix; and the inclusion of such combinatorial topics as BIBDs, Hadamard matrices, and strongly regular graphs. Also included are McCoy's theorem about matrices with property P, the Bruck-Ryser-Chowla theorem on the existence of block designs, and an introduction to Markov chains. This book is intended for those who are familiar with the linear algebra covered in a typical first course and are interested in learning more advanced results. |
| linear algebra and matrix theory: Applied Linear Algebra and Matrix Analysis Thomas S. Shores, 2007-03-12 This new book offers a fresh approach to matrix and linear algebra by providing a balanced blend of applications, theory, and computation, while highlighting their interdependence. Intended for a one-semester course, Applied Linear Algebra and Matrix Analysis places special emphasis on linear algebra as an experimental science, with numerous examples, computer exercises, and projects. While the flavor is heavily computational and experimental, the text is independent of specific hardware or software platforms. Throughout the book, significant motivating examples are woven into the text, and each section ends with a set of exercises. |
| linear algebra and matrix theory: Elementary Linear Algebra Kenneth Kuttler, 2012-01-10 This is an introduction to linear algebra. The main part of the book features row operations and everything is done in terms of the row reduced echelon form and specific algorithms. At the end, the more abstract notions of vector spaces and linear transformations on vector spaces are presented. However, this is intended to be a first course in linear algebra for students who are sophomores or juniors who have had a course in one variable calculus and a reasonable background in college algebra. I have given complete proofs of all the fundamental ideas, but some topics such as Markov matrices are not complete in this book but receive a plausible introduction. The book contains a complete treatment of determinants and a simple proof of the Cayley Hamilton theorem although these are optional topics. The Jordan form is presented as an appendix. I see this theorem as the beginning of more advanced topics in linear algebra and not really part of a beginning linear algebra course. There are extensions of many of the topics of this book in my on line book. I have also not emphasized that linear algebra can be carried out with any field although there is an optional section on this topic, most of the book being devoted to either the real numbers or the complex numbers. It seems to me this is a reasonable specialization for a first course in linear algebra. |
| linear algebra and matrix theory: Matrix Algebra for Linear Models Marvin H. J. Gruber, 2013-12-31 A self-contained introduction to matrix analysis theory and applications in the field of statistics Comprehensive in scope, Matrix Algebra for Linear Models offers a succinct summary of matrix theory and its related applications to statistics, especially linear models. The book provides a unified presentation of the mathematical properties and statistical applications of matrices in order to define and manipulate data. Written for theoretical and applied statisticians, the book utilizes multiple numerical examples to illustrate key ideas, methods, and techniques crucial to understanding matrix algebra’s application in linear models. Matrix Algebra for Linear Models expertly balances concepts and methods allowing for a side-by-side presentation of matrix theory and its linear model applications. Including concise summaries on each topic, the book also features: Methods of deriving results from the properties of eigenvalues and the singular value decomposition Solutions to matrix optimization problems for obtaining more efficient biased estimators for parameters in linear regression models A section on the generalized singular value decomposition Multiple chapter exercises with selected answers to enhance understanding of the presented material Matrix Algebra for Linear Models is an ideal textbook for advanced undergraduate and graduate-level courses on statistics, matrices, and linear algebra. The book is also an excellent reference for statisticians, engineers, economists, and readers interested in the linear statistical model. |
| linear algebra and matrix theory: Advanced Linear Algebra Steven Roman, 2007-12-31 Covers a notably broad range of topics, including some topics not generally found in linear algebra books Contains a discussion of the basics of linear algebra |
| linear algebra and matrix theory: Matrix Theory Robert Piziak, P.L. Odell, 2007-02-22 In 1990, the National Science Foundation recommended that every college mathematics curriculum should include a second course in linear algebra. In answer to this recommendation, Matrix Theory: From Generalized Inverses to Jordan Form provides the material for a second semester of linear algebra that probes introductory linear algebra concepts while also exploring topics not typically covered in a sophomore-level class. Tailoring the material to advanced undergraduate and beginning graduate students, the authors offer instructors flexibility in choosing topics from the book. The text first focuses on the central problem of linear algebra: solving systems of linear equations. It then discusses LU factorization, derives Sylvester's rank formula, introduces full-rank factorization, and describes generalized inverses. After discussions on norms, QR factorization, and orthogonality, the authors prove the important spectral theorem. They also highlight the primary decomposition theorem, Schur's triangularization theorem, singular value decomposition, and the Jordan canonical form theorem. The book concludes with a chapter on multilinear algebra. With this classroom-tested text students can delve into elementary linear algebra ideas at a deeper level and prepare for further study in matrix theory and abstract algebra. |
| linear algebra and matrix theory: Matrices and Linear Algebra Hans Schneider, George Phillip Barker, 1989-01-01 Linear algebra is one of the central disciplines in mathematics. A student of pure mathematics must know linear algebra if he is to continue with modern algebra or functional analysis. Much of the mathematics now taught to engineers and physicists requires it. This well-known and highly regarded text makes the subject accessible to undergraduates with little mathematical experience. Written mainly for students in physics, engineering, economics, and other fields outside mathematics, the book gives the theory of matrices and applications to systems of linear equations, as well as many related topics such as determinants, eigenvalues, and differential equations. Table of Contents: l. The Algebra of Matrices 2. Linear Equations 3. Vector Spaces 4. Determinants 5. Linear Transformations 6. Eigenvalues and Eigenvectors 7. Inner Product Spaces 8. Applications to Differential Equations For the second edition, the authors added several exercises in each chapter and a brand new section in Chapter 7. The exercises, which are both true-false and multiple-choice, will enable the student to test his grasp of the definitions and theorems in the chapter. The new section in Chapter 7 illustrates the geometric content of Sylvester's Theorem by means of conic sections and quadric surfaces. 6 line drawings. lndex. Two prefaces. Answer section. |
| linear algebra and matrix theory: Matrix Theory Joel N. Franklin, 2012-07-31 Mathematically rigorous introduction covers vector and matrix norms, the condition-number of a matrix, positive and irreducible matrices, much more. Only elementary algebra and calculus required. Includes problem-solving exercises. 1968 edition. |
| linear algebra and matrix theory: Introduction to Matrix Theory Arindama Singh, 2021-08-16 This book is designed to serve as a textbook for courses offered to undergraduate and postgraduate students enrolled in Mathematics. Using elementary row operations and Gram-Schmidt orthogonalization as basic tools the text develops characterization of equivalence and similarity, and various factorizations such as rank factorization, OR-factorization, Schurtriangularization, Diagonalization of normal matrices, Jordan decomposition, singular value decomposition, and polar decomposition. Along with Gauss-Jordan elimination for linear systems, it also discusses best approximations and least-squares solutions. The book includes norms on matrices as a means to deal with iterative solutions of linear systems and exponential of a matrix. The topics in the book are dealt with in a lively manner. Each section of the book has exercises to reinforce the concepts, and problems have been added at the end of each chapter. Most of these problems are theoretical, and they do not fit into the running text linearly. The detailed coverage and pedagogical tools make this an ideal textbook for students and researchers enrolled in senior undergraduate and beginning postgraduate mathematics courses. |
| linear algebra and matrix theory: Matrix Analysis Roger A. Horn, Charles R. Johnson, 1990-02-23 Matrix Analysis presents the classical and recent results for matrix analysis that have proved to be important to applied mathematics. |
| linear algebra and matrix theory: Matrix Algebra James E. Gentle, |
| linear algebra and matrix theory: A First Course in Linear Algebra Kenneth Kuttler, Ilijas Farah, 2020 A First Course in Linear Algebra, originally by K. Kuttler, has been redesigned by the Lyryx editorial team as a first course for the general students who have an understanding of basic high school algebra and intend to be users of linear algebra methods in their profession, from business & economics to science students. All major topics of linear algebra are available in detail, as well as justifications of important results. In addition, connections to topics covered in advanced courses are introduced. The textbook is designed in a modular fashion to maximize flexibility and facilitate adaptation to a given course outline and student profile. Each chapter begins with a list of student learning outcomes, and examples and diagrams are given throughout the text to reinforce ideas and provide guidance on how to approach various problems. Suggested exercises are included at the end of each section, with selected answers at the end of the textbook.--BCcampus website. |
| linear algebra and matrix theory: Linear Algebra for Control Theory Paul Van Dooren, Bostwick Wyman, 2012-12-06 During the past decade the interaction between control theory and linear algebra has been ever increasing, giving rise to new results in both areas. As a natural outflow of this research, this book presents information on this interdisciplinary area. The cross-fertilization between control and linear algebra can be found in subfields such as Numerical Linear Algebra, Canonical Forms, Ring-theoretic Methods, Matrix Theory, and Robust Control. This book's editors were challenged to present the latest results in these areas and to find points of common interest. This volume reflects very nicely the interaction: the range of topics seems very wide indeed, but the basic problems and techniques are always closely connected. And the common denominator in all of this is, of course, linear algebra. This book is suitable for both mathematicians and students. |
| linear algebra and matrix theory: Linear Algebra and Matrix Analysis for Statistics Sudipto Banerjee, Anindya Roy, 2014-06-06 Assuming no prior knowledge of linear algebra, this self-contained text offers a gradual exposition to linear algebra without sacrificing the rigor of the subject. It presents both the vector space approach and the canonical forms in matrix theory. The book covers important topics in linear algebra that are useful for statisticians, including the concept of rank, the fundamental theorem of linear algebra, projectors, and quadratic forms. It also provides an extensive collection of exercises on theoretical concepts and numerical computations. |
| linear algebra and matrix theory: A Survey of Matrix Theory and Matrix Inequalities Marvin Marcus, Henryk Minc, 1992-01-01 Concise, masterly survey of a substantial part of modern matrix theory introduces broad range of ideas involving both matrix theory and matrix inequalities. Also, convexity and matrices, localization of characteristic roots, proofs of classical theorems and results in contemporary research literature, more. Undergraduate-level. 1969 edition. Bibliography. |
| linear algebra and matrix theory: No Bullshit Guide to Linear Algebra Ivan Savov, 2020-10-25 This textbook covers the material for an undergraduate linear algebra course: vectors, matrices, linear transformations, computational techniques, geometric constructions, and theoretical foundations. The explanations are given in an informal conversational tone. The book also contains 100+ problems and exercises with answers and solutions. A special feature of this textbook is the prerequisites chapter that covers topics from high school math, which are necessary for learning linear algebra. The presence of this chapter makes the book suitable for beginners and the general audience-readers need not be math experts to read this book. Another unique aspect of the book are the applications chapters (Ch 7, 8, and 9) that discuss applications of linear algebra to engineering, computer science, economics, chemistry, machine learning, and even quantum mechanics. |
| linear algebra and matrix theory: Coding the Matrix Philip N. Klein, 2013-07 An engaging introduction to vectors and matrices and the algorithms that operate on them, intended for the student who knows how to program. Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by doing, writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank (Google's ranking algorithm), and cancer detection from cell features. A companion web site, codingthematrix.com provides data and support code. Most of the assignments can be auto-graded online. Over two hundred illustrations, including a selection of relevant xkcd comics. Chapters: The Function, The Field, The Vector, The Vector Space, The Matrix, The Basis, Dimension, Gaussian Elimination, The Inner Product, Special Bases, The Singular Value Decomposition, The Eigenvector, The Linear Program A new edition of this text, incorporating corrections and an expanded index, has been issued as of September 4, 2013, and will soon be available on Amazon. |
| linear algebra and matrix theory: Applied Engineering Analysis Tai-Ran Hsu, 2018-04-30 A resource book applying mathematics to solve engineering problems Applied Engineering Analysis is a concise textbookwhich demonstrates how toapply mathematics to solve engineering problems. It begins with an overview of engineering analysis and an introduction to mathematical modeling, followed by vector calculus, matrices and linear algebra, and applications of first and second order differential equations. Fourier series and Laplace transform are also covered, along with partial differential equations, numerical solutions to nonlinear and differential equations and an introduction to finite element analysis. The book also covers statistics with applications to design and statistical process controls. Drawing on the author's extensive industry and teaching experience, spanning 40 years, the book takes a pedagogical approach and includes examples, case studies and end of chapter problems. It is also accompanied by a website hosting a solutions manual and PowerPoint slides for instructors. Key features: Strong emphasis on deriving equations, not just solving given equations, for the solution of engineering problems. Examples and problems of a practical nature with illustrations to enhance student’s self-learning. Numerical methods and techniques, including finite element analysis. Includes coverage of statistical methods for probabilistic design analysis of structures and statistical process control (SPC). Applied Engineering Analysis is a resource book for engineering students and professionals to learn how to apply the mathematics experience and skills that they have already acquired to their engineering profession for innovation, problem solving, and decision making. |
| linear algebra and matrix theory: Numerical Linear Algebra and Matrix Factorizations Tom Lyche, 2020-03-02 After reading this book, students should be able to analyze computational problems in linear algebra such as linear systems, least squares- and eigenvalue problems, and to develop their own algorithms for solving them. Since these problems can be large and difficult to handle, much can be gained by understanding and taking advantage of special structures. This in turn requires a good grasp of basic numerical linear algebra and matrix factorizations. Factoring a matrix into a product of simpler matrices is a crucial tool in numerical linear algebra, because it allows us to tackle complex problems by solving a sequence of easier ones. The main characteristics of this book are as follows: It is self-contained, only assuming that readers have completed first-year calculus and an introductory course on linear algebra, and that they have some experience with solving mathematical problems on a computer. The book provides detailed proofs of virtually all results. Further, its respective parts can be used independently, making it suitable for self-study. The book consists of 15 chapters, divided into five thematically oriented parts. The chapters are designed for a one-week-per-chapter, one-semester course. To facilitate self-study, an introductory chapter includes a brief review of linear algebra. |
| linear algebra and matrix theory: Linear Algebra: Theory, Intuition, Code Mike X. Cohen, 2021-02 Linear algebra is perhaps the most important branch of mathematics for computational sciences, including machine learning, AI, data science, statistics, simulations, computer graphics, multivariate analyses, matrix decompositions, signal processing, and so on.The way linear algebra is presented in traditional textbooks is different from how professionals use linear algebra in computers to solve real-world applications in machine learning, data science, statistics, and signal processing. For example, the determinant of a matrix is important for linear algebra theory, but should you actually use the determinant in practical applications? The answer may surprise you!If you are interested in learning the mathematical concepts linear algebra and matrix analysis, but also want to apply those concepts to data analyses on computers (e.g., statistics or signal processing), then this book is for you. You'll see all the math concepts implemented in MATLAB and in Python.Unique aspects of this book: - Clear and comprehensible explanations of concepts and theories in linear algebra. - Several distinct explanations of the same ideas, which is a proven technique for learning. - Visualization using graphs, which strengthens the geometric intuition of linear algebra. - Implementations in MATLAB and Python. Com'on, in the real world, you never solve math problems by hand! You need to know how to implement math in software! - Beginner to intermediate topics, including vectors, matrix multiplications, least-squares projections, eigendecomposition, and singular-value decomposition. - Strong focus on modern applications-oriented aspects of linear algebra and matrix analysis. - Intuitive visual explanations of diagonalization, eigenvalues and eigenvectors, and singular value decomposition. - Codes (MATLAB and Python) are provided to help you understand and apply linear algebra concepts on computers. - A combination of hand-solved exercises and more advanced code challenges. Math is not a spectator sport! |
| linear algebra and matrix theory: Matrices and Linear Transformations Charles G. Cullen, 2012-09-20 Undergraduate-level introduction to linear algebra and matrix theory. Explores matrices and linear systems, vector spaces, determinants, spectral decomposition, Jordan canonical form, much more. Over 375 problems. Selected answers. 1972 edition. |
Linear Algebra | Mathematics | MIT OpenCourseWare
Course Description. This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.
Linear Algebra and Matrix Theory | ScienceDirect
This chapter discusses real coordinate spaces. There are various approaches to linear algebra and different approaches emphasize different aspects of the subject such as matrices, applications, or computational methods. As presented in the chapter, linear algebra is in essence a study of vector spaces, and this study of vector spaces is ...
Matrix Theory and Linear Algebra - Dalhousie University
26 Oct 2018 · Matrix Theory and Linear Algebra is an introduction to linear algebra for students in the first or second year of university. The book contains enough material for a 2-semester course. Major topics of linear algebra are presented in detail, and many applications are given.
Linear Algebra | Mathematics | MIT OpenCourseWare
This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering.
MATH 113: Linear Algebra and Matrix Theory - Stanford University
Course description: This is a rigorous proof-based course course on linear algebra. List of topics: vector spaces, linear independence, basis, span, dimension ; linear maps, matrices, nullspace and range, invertibility and isomorphism ; products and quotients of vector spaces, duality ; volume and determinants
Lecture Notes for Linear Algebra (2021) - MIT Mathematics
Part 1 : Basic Ideas of Linear Algebra. 1.1 Linear Combinations of Vectors. 1.2 Dot Products v · w and Lengths || v || and Angles θ. 1.3 Matrices Multiplying Vectors : A times x. 1.4 Column Space and Row Space of A. 1.5 Dependent and Independent Columns. 1.6 Matrix-Matrix Multiplication AB. 1.7 Factoring A into CR : Column rank = r = Row rank.
What is the difference between matrix theory and linear algebra?
13 Apr 2017 · Currently, I'm taking matrix theory, and our textbook is Strang's Linear Algebra. Besides matrix theory, which all engineers must take, there exists linear algebra I and II for math majors. What is the difference, if any, between matrix theory and linear algebra?
Linear Algebra, Theory And Applications - Open Textbook Library
29 Jun 2020 · This is a book on linear algebra and matrix theory. While it is self contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed that the reader has had calculus.
Syllabus | Linear Algebra | Mathematics | MIT OpenCourseWare
This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines. Linear algebra is a branch of mathematics that studies systems of linear equations and the properties of matrices.
M341: Linear algebra and matrix theory, Spring 2021
Specific topics to be covered include vectors and matrices, systems of linear equations and Gaussian elimination, eigenvalues and eigenvectors, determinants, vector spaces, linear transformations, and orthogonality. The syllabus provides the …
Advanced Linear and Matrix Algebra | SpringerLink
Building on a first course in linear algebra, this book offers readers a deeper understanding of abstract structures, matrix decompositions, multilinearity, and tensors. Concepts draw on concrete examples throughout, offering accessible pathways to advanced techniques.
LINEAR ALGEBRA AND MATRICES - University of Illinois Chicago
Linear algebra and matrix theory, abbreviated here as LAMT, is a foundation for many advanced topics in mathematics, and an essential tool for computer sciences, physics, engineering, bioinformatics, economics, and social sciences.
Matrix Theory: Basic Results and Techniques | SpringerLink
The aim of this book is to concisely present fundamental ideas, results, and techniques in linear algebra and mainly matrix theory. The book contains ten chapters covering various topics ranging from similarity and special types of matrices to Schur complements and matrix normality.
Linear Algebra and Matrix Theory - UH
Linear Algebra and Matrix Theory. Chapter 1 - Linear Systems, Matrices and Determinants. This is a very brief outline of some basic definitions and theorems of linear. algebra. We will assume that you know elementary facts such as how to add. two matrices, how to multiply a matrix by a number, how to multiply two.
Linear Algebra: Linear Systems and Matrix Equations - Coursera
We show in this section that answering questions about linear combinations turns out to be equivalent to solving a system of linear equations, underlying the deep connections of linear algebra. We then introduce the notion of a matrix as a function on vectors.
Introduction to Matrix Theory - SpringerLink
“This is a concise, concrete introduction to matrix theory and linear algebra, designed as a one-semester course for science and engineering students. … The book has a reasonable number of exercises.” (Allen Stenger, MAA Reviews, December 12, 2021)
Introduction to Linear and Matrix Algebra | SpringerLink
This textbook emphasizes the interplay between algebra and geometry to motivate the study of linear algebra. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book.
What is the difference between matrix theory and linear algebra?
Matrix theory is the specialization of linear algebra to the case of finite dimensional vector spaces and doing explicit manipulations after fixing a basis. More precisely: The algebra of $n \times n$ matrices with coefficients in a field $F$ is isomorphic to the algebra of $F$-linear homomorphisms from an $n$-dimensional vector space $V$ over ...
Lecture Notes 1: Matrix Algebra Part A: Vectors and Matrices
Using Matrix Notation, I Matrix notation allows the two equations 1x + 1y = b 1 1x 1y = b 2 to be expressed as 1 1 1 1 x y = b 1 b 2 or as Az = b, where A = 1 1 1 1 ; z = x y ; and b = b 1 b 2 : Here A;z;b are respectively: (i) thecoe cient matrix; (ii) thevector of unknowns; (iii) …
Linear Algebra - SpringerLink
Provides a matrix-oriented approach to the theory of linear algebra including all details and proofs. Improves intuition for students in their first contact with abstract concepts. Analyzes detailed examples from application, contains ‘MATLAB-Minutes’ and …
Linear Algebra | Mathematics | MIT OpenCourseWare
Course Description. This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, …
Linear Algebra and Matrix Theory | ScienceDirect
This chapter discusses real coordinate spaces. There are various approaches to linear algebra and different approaches emphasize different aspects of the subject such as matrices, …
Matrix Theory and Linear Algebra - Dalhousie University
26 Oct 2018 · Matrix Theory and Linear Algebra is an introduction to linear algebra for students in the first or second year of university. The book contains enough material for a 2-semester …
Linear Algebra | Mathematics | MIT OpenCourseWare
This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering.
MATH 113: Linear Algebra and Matrix Theory - Stanford University
Course description: This is a rigorous proof-based course course on linear algebra. List of topics: vector spaces, linear independence, basis, span, dimension ; linear maps, matrices, nullspace …
Lecture Notes for Linear Algebra (2021) - MIT Mathematics
Part 1 : Basic Ideas of Linear Algebra. 1.1 Linear Combinations of Vectors. 1.2 Dot Products v · w and Lengths || v || and Angles θ. 1.3 Matrices Multiplying Vectors : A times x. 1.4 Column …
What is the difference between matrix theory and linear algebra?
13 Apr 2017 · Currently, I'm taking matrix theory, and our textbook is Strang's Linear Algebra. Besides matrix theory, which all engineers must take, there exists linear algebra I and II for …
Linear Algebra, Theory And Applications - Open Textbook Library
29 Jun 2020 · This is a book on linear algebra and matrix theory. While it is self contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed …
Syllabus | Linear Algebra | Mathematics | MIT OpenCourseWare
This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines. Linear algebra is a branch of mathematics that studies systems of linear equations …
M341: Linear algebra and matrix theory, Spring 2021
Specific topics to be covered include vectors and matrices, systems of linear equations and Gaussian elimination, eigenvalues and eigenvectors, determinants, vector spaces, linear …
Advanced Linear and Matrix Algebra | SpringerLink
Building on a first course in linear algebra, this book offers readers a deeper understanding of abstract structures, matrix decompositions, multilinearity, and tensors. Concepts draw on …
LINEAR ALGEBRA AND MATRICES - University of Illinois Chicago
Linear algebra and matrix theory, abbreviated here as LAMT, is a foundation for many advanced topics in mathematics, and an essential tool for computer sciences, physics, engineering, …
Matrix Theory: Basic Results and Techniques | SpringerLink
The aim of this book is to concisely present fundamental ideas, results, and techniques in linear algebra and mainly matrix theory. The book contains ten chapters covering various topics …
Linear Algebra and Matrix Theory - UH
Linear Algebra and Matrix Theory. Chapter 1 - Linear Systems, Matrices and Determinants. This is a very brief outline of some basic definitions and theorems of linear. algebra. We will …
Linear Algebra: Linear Systems and Matrix Equations - Coursera
We show in this section that answering questions about linear combinations turns out to be equivalent to solving a system of linear equations, underlying the deep connections of linear …
Introduction to Matrix Theory - SpringerLink
“This is a concise, concrete introduction to matrix theory and linear algebra, designed as a one-semester course for science and engineering students. … The book has a reasonable number …
Introduction to Linear and Matrix Algebra | SpringerLink
This textbook emphasizes the interplay between algebra and geometry to motivate the study of linear algebra. Matrices and linear transformations are presented as two sides of the same …
What is the difference between matrix theory and linear algebra?
Matrix theory is the specialization of linear algebra to the case of finite dimensional vector spaces and doing explicit manipulations after fixing a basis. More precisely: The algebra of $n \times …
Lecture Notes 1: Matrix Algebra Part A: Vectors and Matrices
Using Matrix Notation, I Matrix notation allows the two equations 1x + 1y = b 1 1x 1y = b 2 to be expressed as 1 1 1 1 x y = b 1 b 2 or as Az = b, where A = 1 1 1 1 ; z = x y ; and b = b 1 b 2 : …
Linear Algebra - SpringerLink
Provides a matrix-oriented approach to the theory of linear algebra including all details and proofs. Improves intuition for students in their first contact with abstract concepts. Analyzes detailed …
