**Best Reference Books on Matrix**, which are used by students of top universities, and colleges. This will help you choose the right book depending on if you are a beginner or an expert. Here is the complete list of

**Matrix Books**with their authors, publishers, and an unbiased review of them as well as links to the Amazon website to directly purchase them. If permissible, you can also download the free PDF books on Matrix below.

## 1. Matrix Computations

1."Iterative Solution Methods" by Owe Axelsson
Book Review: This book provides a comprehensive overview of linear algebra and numerical linear algebra, covering both basic and classic methods. It focuses on the construction of preconditioners and iterative acceleration methods, specifically the conjugate gradient type. Targeted at graduate students and researchers in numerical analysis and applied mathematics, it is also relevant to other fields where linear equation systems are important. The book includes mathematical theories and concepts pertaining to numerical linear algebra.
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2."Computer Solution of Large Linear Systems" by G Meurant
Book Review: The focus of this book is on numerical methods used for solving large, sparse linear systems of equations, particularly those resulting from the discretization of partial differential equations. Both direct and iterative methods are covered, with direct methods including various Gaussian elimination variants suitable for solving differential equations in rectangular domains. The book also explores classical iterative methods such as Jacobi, Gauss-Seidel, and other directional algorithms. In addition, there is a dedicated chapter on multigrid methods, and the book concludes with a discussion of domain decomposition algorithms. This resource is valuable for those in fields where numerical methods are critical, including graduate students and researchers in applied mathematics and related areas.
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3."Matrix Computations" by Golub and C Van Loan
Book Review: This textbook on computer science provides essential information on the mathematical foundation and algorithmic skills necessary for creating numerical software. The book has updated chapters on various topics, including matrix multiplication, parallel matrix computation, CS decomposition, floating-point arithmetic operations, the Gram-Schmidt process, and methods such as GMRES and QMR that address issues with sparse, unsymmetrical linear systems. This book is recommended for anyone interested in numerical software development, computer science, or related fields.
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4."Matrix Perturbation Theory" by G W Stewart and J Sun
Book Review: This book presents an overview of matrix perturbation theory and its concepts, making it a valuable resource for numerical analysts, statisticians, physical scientists, and engineers. The book covers the perturbation theory of linear systems, least square problems, eigenvalue problems, generalized eigenvalue problems, as well as vector and matrix norms, including the theory of unitary invariant norms.
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5."Fundamentals of Matrix Computations" by Watkins D S
Book Review: The focus of this book is on the fundamental concepts of matrix computations, numerical linear algebra algorithms, algorithmic development and their implementation. The book covers various topics such as the Francis QR algorithm, the applications of the Gram-Schmidt algorithm, Golub-Reinsch SVD algorithm derivation, solving the eigenvalue product problem, treatment of the Jacobi-Davidson method, and various iterative methods for solving linear equations. It also uses MATLAB to solve real-world problems in electrical circuits, mass-spring systems, simple partial differential equations, and matrix computations. The book is aimed at researchers and practitioners working in the fields of engineering and computer science.
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6."Introduction to Matrix Computations" by Stewart GW
“Introduction to Matrix Computations” Book Review: This book provides a comprehensive coverage of algorithms used for solving linear systems, linear least squares problems, and eigenvalue problems for matrices that can be stored in the high-speed memory of a computer. The book includes a detailed discussion on the theory of norms and perturbation theory for linear systems, as well as algebraic eigenvalue problems. It is a valuable resource for students, researchers, and professionals alike.
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7."MILESTONES IN MATRIX COMPUTATION" by Chan
“Milestones in Matrix Computation” Book Review: The book is comprised of 21 papers on Matrix Computation, divided into five sections. The first section discusses iterative methods for linear systems, while the second focuses on solving least squares problems. The third section covers matrix factorizations and their applications, while the fourth provides a detailed explanation of orthogonal polynomials and quadrature. The last section delves into eigenvalue problems. This book is an ideal resource for students and researchers in the fields of numerical analysis and scientific computation.
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8."Numerical Methods in Matrix Computations" by Bjorck Ake Bjorck
“Numerical Methods in Matrix Computations” Book Review: The book provides an extensive and current account of contemporary matrix computation techniques. It comprehensively examines the stability, accuracy, and complexity of these methods. The book takes a unified approach to explaining direct and iterative methods for linear systems, least squares, and eigenvalue problems. It is well-suited for advanced undergraduate and graduate courses in scientific computing and applied technical areas.
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9."A Study on the Computation of the Determinants of a 3x3 Matrix" by Assen Awol
“A Study on the Computation of the Determinants of a 3×3 Matrix” Book Review: The focus of this book is the computation of determinants for 3×3 matrices. The book explores a range of methods, including both classic and modern techniques, that provide efficient and straightforward ways to calculate determinants. These methods have significant potential for further research in computing higher order determinants. This book is intended for students, researchers, and professionals who are interested in this topic.
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10."PARALLELISM IN MATRIX COMPUTATIONS" by GALLOPOULOS
“Parallelism in Matrix Computations” Book Review: This book provides an overview of various algorithms for matrix computations with a focus on their parallelism and robustness. It covers fundamental kernels, sparse matrix schemes, and parallel programming paradigms, followed by detailed treatments of dense and special matrix computations, and sparse matrix computations. The final section explores the development of parallel algorithms for matrix functions, including the matrix pseudospectrum and determinant. Prerequisite knowledge of numerical linear algebra, parallel architectures, and programming paradigms is required. The book is designed for graduate courses in the design of parallel algorithms for matrix computations.
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## 2. Matrix Methods and Introduction to Computers

1."An Introduction to Queueing Theory: and Matrix-Analytic Methods" by L Breuer and Dieter Baum
“An Introduction to Queueing Theory: and Matrix-Analytic Methods” Book Review: This book is designed to assist undergraduate students studying queuing theory, specifically those in their final year. It provides comprehensive coverage of queueing models and their applications. The book focuses on presenting only the necessary mathematical foundations to understand the concepts, making it accessible to students with a limited mathematical background.
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2."Matrix Methods of Structural Analysis" by S S Bhavikatti
“Matrix Methods of Structural Analysis” Book Review: This book aims to bridge the gap between structural analysis and classical methods, with a particular emphasis on the stiffness matrix method element approach. The material has been presented in a manner that is accessible to students, with a focus on clarity and ease of understanding.
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3."Matrix-Based Introduction to Multivariate Data Analysis" by Kohei Adachi
“Matrix-Based Introduction to Multivariate Data Analysis” Book Review: This book is intended for undergraduate students in statistics, but it is also useful for graduate students and researchers. The book is designed to help those who are new to matrices understand a variety of multivariate analysis procedures. Each chapter contains numerical examples with plain explanations of their purposes. The book covers the basic principles and also provides in-depth knowledge of the subject.
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4."Introduction to Scientific Computing: A Matrix-Vector Approach Using MATLAB (The MATLAB curriculum series)" by Charles F Van Loan
“Introduction to Scientific Computing: A Matrix-Vector Approach Using MATLAB (The MATLAB curriculum series)” Book Review: The book is an ideal resource for anyone looking to learn scientific computing using MATLAB. The book covers a variety of topics, including matrix algebra, numerical methods, interpolation, differentiation and integration, linear programming, and partial differential equations. The book’s approach is practical, with a focus on using MATLAB to solve real-world problems in science and engineering. Each chapter includes numerous examples and exercises to help readers develop their skills and apply the concepts they have learned.
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5."Introduction to Structural Analysis: Displacement and Force Methods" by S T Mau
“Introduction to Structural Analysis: Displacement and Force Methods” Book Review: The book provides a comprehensive coverage of the basic methods of structural analysis applied to trusses, beams, and rigid frames. The force method of analysis for plane trusses is explained in detail, illustrating force equilibrium, deflection, and other concepts. The book also covers influence lines, non-prismatic members, and the limits of linear and static structural analysis. This material is suitable for students studying introductory courses in structural analysis and for those looking to deepen their understanding of the subject.
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