Matrix Analysis, written by Roger Horn and Charles Johnson, is a comprehensive textbook on linear algebra that is designed for advanced undergraduate and graduate students. Among the best books on matrices, this book provides a modern and sophisticated treatment of matrix theory, an essential mathematical tool for many scientific and engineering disciplines.

Roger Horn is a renowned mathematician and professor emeritus at the University of Utah. He is well known for his contributions to matrix analysis, optimization theory, and computational mathematics. Charles Johnson is also a respected mathematician and professor at the College of William & Mary. He has published extensively on matrix theory, numerical analysis, and discrete mathematics.

The book begins with an introduction to basic matrix algebra and gradually builds up to more advanced topics, including matrix decomposition, matrix functions, and matrix equations. The authors provide a rigorous and detailed exposition of the subject matter, with numerous examples, exercises, and applications to real-world problems.

Matrix Analysis covers a broad range of topics, including positive definite matrices, matrix norms, matrix inequalities, and perturbation theory. It also includes a thorough discussion of spectral theory, which is a powerful tool for understanding the properties of matrices and their applications. The book concludes with a chapter on numerical methods for matrix computation, which is essential for practical applications of matrix theory.

Overall, Matrix Analysis is an excellent resource for students and researchers in mathematics, engineering, physics, and computer science. It provides a comprehensive and up-to-date treatment of matrix theory, with a focus on rigorous mathematical analysis and its applications.

Author: Charles R. Johnson and Roger A. Horn

Link to buy: https://www.amazon.com/gp/aw/d/0521548233/

Ratings: 4.6 out of 5 stars (from 85 reviews)

Best Sellers Rank: #866,813 in Books

#54 in Mathematical Matrices

#169 in Linear Algebra (Books)

#409 in Mathematical Analysis (Books)

Matrices and Linear Algebra is an introductory text on the fundamental concepts and techniques of linear algebra, authored by American mathematician and educator, Hans Schneider and George Phillip Barker. The book, published by Dover Publications in 1986, is a revised and expanded version of the author's earlier work, Introduction to Linear Algebra, which was first published in 1959.

Hans Schneider received his Ph.D. from the University of Chicago in 1951 and went on to teach at various universities, including the University of California, Berkeley, and the University of Wisconsin-Madison. He authored several textbooks on linear algebra and related subjects, including Linear Algebra, Algebra, and Elementary Linear Algebra.

The book is designed for students with little or no prior knowledge of linear algebra and is suitable for self-study or as a supplement to a course in linear algebra. It covers the basic concepts of linear equations, matrices, determinants, vector spaces, linear transformations, and eigenvalues and eigenvectors, with an emphasis on the practical applications of these concepts.

The book's introduction provides a brief overview of linear algebra, its historical development, and its applications in various fields such as physics, engineering, and computer science. It also explains the importance of matrices, which are central to the study of linear algebra, and how they can be used to solve systems of linear equations and represent linear transformations.

Overall, Matrices and Linear Algebra is an accessible and comprehensive introduction to linear algebra that provides a solid foundation for further study in the subject. Its clear and concise presentation, numerous examples and exercises, and practical applications make it a valuable resource for students and professionals alike. The book is one of the best books on matrices.

Author: Hans Schneider and George Phillip Barker

Link to buy: https://www.amazon.com/Matrices-Linear-Algebra-Dover-Mathematics/dp/0486660141/

Ratings: 4.4 out of 5 stars (from 57 reviews)

Best Sellers Rank: #311,467 in Books

#22 in Mathematical Matrices

#60 in Linear Algebra (Books)

#148 in Algebra & Trigonometry

Coding the Matrix, authored by Philip N. Klein, is a comprehensive guide to the mathematical foundations of computer science. The book offers an innovative and interactive approach to understanding linear algebra and its applications in computer science.

Philip N. Klein is a Professor of Computer Science at Brown University, where he teaches courses on algorithm design, programming languages, and theoretical computer science. He has a Ph.D. in Computer Science from Cornell University and has published numerous papers on topics ranging from computational geometry to quantum computing.

In the book's introduction, Klein explains that linear algebra is a crucial tool in computer science, used in a variety of applications such as computer graphics, cryptography, and machine learning. However, he notes that many students find it difficult to learn linear algebra, as traditional approaches often rely heavily on abstract concepts and formal proofs.

To address this challenge, Klein takes a novel approach to teach linear algebra, using Python programming and interactive examples to illustrate key concepts. The book is organized around a series of "programming assignments," which guide readers through the process of implementing algorithms and solving problems using linear algebra.

Throughout the book, Klein emphasizes the practical applications of linear algebra, showing readers how it can be used to solve real-world problems in computer science. With its engaging approach and emphasis on hands-on learning, Coding the Matrix is an invaluable resource for students, educators, and anyone interested in understanding the mathematical foundations of computer science.

Author: Philip N. Klein

Link to buy: https://www.amazon.com/gp/aw/d/0615880991/

Ratings: 4.5 out of 5 stars (from 161 reviews)

Best Sellers Rank: #109,226 in Books

#8 in Mathematical Matrices

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Matrix computations is an essential topic in modern mathematics, computer science, and engineering. It deals with the theory and application of matrix algebra and its algorithms, providing a foundation for many fields, including data analysis, numerical analysis, optimization, and scientific computing. The book "Matrix Computations," published in 2013 by Johns Hopkins University Press, is an authoritative and comprehensive introduction to this subject. It is considered one of the best books on matrices.

The book is authored by Gene H. Golub and Charles F. Van Loan, who are both distinguished professors in the field of numerical analysis. Gene H. Golub was a professor of computer science at Stanford University and is widely regarded as one of the pioneers in the development of matrix computations. Charles F. Van Loan is a professor of computer science at Cornell University and has made significant contributions to the field of numerical linear algebra.

The book's introduction explains that matrix computations have become an essential tool for solving mathematical problems arising in many fields of science and engineering. The authors provide a thorough treatment of the subject, covering topics such as matrix factorizations, iterative methods, eigenvalue and singular value computations, and applications to data analysis and optimization. The book is suitable for advanced undergraduate and graduate students in mathematics, computer science, and engineering, as well as researchers and practitioners in these fields.

The book's approach is both theoretical and practical, with many examples and exercises included to aid in understanding the concepts and algorithms. The authors also provide MATLAB code for many of the algorithms discussed in the book, making it an excellent resource for those interested in implementing the methods in practice.

In summary, "Matrix Computations" is an essential reference for anyone interested in matrix algebra and its applications. Its comprehensive coverage, clear exposition, and practical examples make it an excellent resource for students, researchers, and practitioners in mathematics, computer science, and engineering.

Author: Charles F. Van Loan and Gene H. Golub

Link to buy: https://www.amazon.com/Computations-Hopkins-Studies-Mathematical-Sciences/dp/1421407949/

Ratings: 4.4 out of 5 stars (from 97 reviews)

Best Sellers Rank: #265,433 in Books

#16 in Mathematical Matrices

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#729 in Applied Mathematics (Books)

Schaum's Outline of Matrix Operations is a comprehensive guide to matrices that has been helping students for over 25 years. The book, written by Richard Bronson and Gabriel B. Costa, offers a clear and concise explanation of the essential concepts, techniques, and applications of matrix theory.

Richard Bronson, the primary author of the book, is a well-respected professor of mathematics who has been teaching for over 30 years. He has also written several other books on mathematical topics, including Schaum's Outline of Differential Equations and Schaum's Outline of Linear Algebra. Gabriel B. Costa, the co-author of the book, is a professor of mathematics at the University of California, Santa Barbara, and has written several other books on numerical analysis and computational mathematics.

The book begins by introducing the basics of matrix algebra, including addition, subtraction, multiplication, and division of matrices. It then delves into more advanced topics, such as determinants, inverse matrices, and eigenvalues and eigenvectors. The book also covers the applications of matrices in various fields, including physics, engineering, and computer science.

One of the most significant advantages of Schaum's Outline of Matrix Operations is its emphasis on problem-solving. The authors have included over 600 fully solved problems in the book, as well as hundreds of additional practice problems for students to work through on their own. The book also includes clear explanations of each step in the problem-solving process, making it an excellent resource for self-study or as a supplement to a traditional classroom setting.

Overall, Schaum's Outline of Matrix Operations is an excellent resource for anyone looking to master the concepts of matrix theory. Its clear explanations, numerous solved problems, and real-world applications make it an essential addition to any student's library.

Author: Richard Bronson

Link to buy: https://www.amazon.com/Schaums-Outline-Matrix-Operations-Outlines/dp/0071756043/

Ratings: 4.6 out of 5 stars (from 65 reviews)

Best Sellers Rank: #611,671 in Books

#44 in Mathematical Matrices

#111 in Linear Algebra (Books)

#3,579 in Study Guides (Books)

Fundamentals of Matrix Computations, one of the best books on matrices, is a comprehensive guide to the mathematical theory and practical applications of matrix computations. Authored by David S. Watkins, a renowned expert in numerical analysis and matrix computations, this book provides a clear and concise introduction to the subject matter. The book covers a wide range of topics, from basic matrix algebra and linear equations to advanced topics such as eigenvalues and singular value decomposition.

David S. Watkins is a Professor Emeritus of Mathematics at Washington State University, where he taught for over three decades. He received his Ph.D. in Mathematics from the University of California, Los Angeles, and has published numerous papers and articles in the field of matrix computations. In addition to his academic pursuits, Watkins has also consulted for a variety of companies and organizations, including Boeing, NASA, and the U.S. Navy.

The book begins with an introduction to matrix algebra and the solution of linear equations using Gaussian elimination. From there, the author progresses to more advanced topics such as eigenvalues and eigenvectors, diagonalization, and singular value decomposition. The book also covers iterative methods for solving linear equations and eigenvalue problems, as well as the numerical solution of differential equations using matrices.

One of the strengths of Fundamentals of Matrix Computations is its emphasis on practical applications. Throughout the book, the author provides real-world examples and exercises that help the reader understand the relevance of the theory to their own work. The book also includes MATLAB code for many of the algorithms and numerical methods discussed, making it a valuable resource for anyone working in the field of numerical analysis or scientific computing.

Overall, Fundamentals of Matrix Computations is an essential reference for anyone interested in the theory and practice of matrix computations. With its clear explanations, practical examples, and emphasis on real-world applications, it is an excellent resource for students, researchers, and practitioners alike.

Author: David S. Watkins

Link to buy: https://www.amazon.com/Fundamentals-Matrix-Computations-David-Watkins/dp/0470528338/

Ratings: 4.4 out of 5 stars (from 22 reviews)

Best Sellers Rank: #396,603 in Books

#26 in Mathematical Matrices

#74 in Linear Algebra (Books)

#188 in Algebra & Trigonometry