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Matrix Algebra Using MINimal MATlab

Author : Joel W. Robbin

Publisher : CRC Press

Page : 560 pages

File Size : 34,50 MB

Release : 2018-10-08

Category : Mathematics

ISBN : 1439864772

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Book Description

The strength of this textbook lies in the careful exposition of mathematical thinking, basic set-theoretic notions, and proof techniques combined with contemporary numerical methods used throughout the book. A basic version of computer programs compatible with the widely used program MatLab, and exercises are provided on a disk included with the book.Warmup * Matrix Operations * Invertible Matrices * Subspaces * Rank and Dimension * Geometry * Determinants-I * Diagonalization * Differential Equations * Hermitian Matrices * Triangular Matrices * Unitary Matrices * Block Diagonalization * Jordan Normal Form * Determinants-II * Proofs * Mathematical Induction†* Summary of MINIMAT * Answers * MINIMAT Tutorial (PC Version)



Linear Algebra and Matrix Computations with MATLAB®

Author : Dingyü Xue

Publisher : Walter de Gruyter GmbH & Co KG

Page : 361 pages

File Size : 16,69 MB

Release : 2020-03-23

Category : Computers

ISBN : 3110663716

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Book Description

This book focuses the solutions of linear algebra and matrix analysis problems, with the exclusive use of MATLAB. The topics include representations, fundamental analysis, transformations of matrices, matrix equation solutions as well as matrix functions. Attempts on matrix and linear algebra applications are also explored.



Matrices and MATLAB

Author : Marvin Marcus

Publisher :

Page : 738 pages

File Size : 34,99 MB

Release : 1993

Category : MATLAB.

ISBN :

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Book Description

This thorough exploration of all aspects of modern matrix theory integrates the use of MatLab(tm) from the beginning.



Scalar, Vector, and Matrix Mathematics

Author : Dennis S. Bernstein

Publisher : Princeton University Press

Page : 1593 pages

File Size : 15,56 MB

Release : 2018-02-27

Category : Mathematics

ISBN : 0691176531

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Book Description

The essential reference book on matrices—now fully updated and expanded, with new material on scalar and vector mathematics Since its initial publication, this book has become the essential reference for users of matrices in all branches of engineering, science, and applied mathematics. In this revised and expanded edition, Dennis Bernstein combines extensive material on scalar and vector mathematics with the latest results in matrix theory to make this the most comprehensive, current, and easy-to-use book on the subject. Each chapter describes relevant theoretical background followed by specialized results. Hundreds of identities, inequalities, and facts are stated clearly and rigorously, with cross-references, citations to the literature, and helpful comments. Beginning with preliminaries on sets, logic, relations, and functions, this unique compendium covers all the major topics in matrix theory, such as transformations and decompositions, polynomial matrices, generalized inverses, and norms. Additional topics include graphs, groups, convex functions, polynomials, and linear systems. The book also features a wealth of new material on scalar inequalities, geometry, combinatorics, series, integrals, and more. Now more comprehensive than ever, Scalar, Vector, and Matrix Mathematics includes a detailed list of symbols, a summary of notation and conventions, an extensive bibliography and author index with page references, and an exhaustive subject index. Fully updated and expanded with new material on scalar and vector mathematics Covers the latest results in matrix theory Provides a list of symbols and a summary of conventions for easy and precise use Includes an extensive bibliography with back-referencing plus an author index



Matrix Mathematics

Author : Dennis S. Bernstein

Publisher : Princeton University Press

Page : 1182 pages

File Size : 26,52 MB

Release : 2009-07-06

Category : Mathematics

ISBN : 1400833345

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Book Description

When first published in 2005, Matrix Mathematics quickly became the essential reference book for users of matrices in all branches of engineering, science, and applied mathematics. In this fully updated and expanded edition, the author brings together the latest results on matrix theory to make this the most complete, current, and easy-to-use book on matrices. Each chapter describes relevant background theory followed by specialized results. Hundreds of identities, inequalities, and matrix facts are stated clearly and rigorously with cross references, citations to the literature, and illuminating remarks. Beginning with preliminaries on sets, functions, and relations,Matrix Mathematics covers all of the major topics in matrix theory, including matrix transformations; polynomial matrices; matrix decompositions; generalized inverses; Kronecker and Schur algebra; positive-semidefinite matrices; vector and matrix norms; the matrix exponential and stability theory; and linear systems and control theory. Also included are a detailed list of symbols, a summary of notation and conventions, an extensive bibliography and author index with page references, and an exhaustive subject index. This significantly expanded edition of Matrix Mathematics features a wealth of new material on graphs, scalar identities and inequalities, alternative partial orderings, matrix pencils, finite groups, zeros of multivariable transfer functions, roots of polynomials, convex functions, and matrix norms. Covers hundreds of important and useful results on matrix theory, many never before available in any book Provides a list of symbols and a summary of conventions for easy use Includes an extensive collection of scalar identities and inequalities Features a detailed bibliography and author index with page references Includes an exhaustive subject index with cross-referencing



Numerical Linear Algebra with Applications

Author : William Ford

Publisher : Academic Press

Page : 629 pages

File Size : 37,25 MB

Release : 2014-09-14

Category : Mathematics

ISBN : 0123947847

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Book Description

Numerical Linear Algebra with Applications is designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, using MATLAB as the vehicle for computation. The book contains all the material necessary for a first year graduate or advanced undergraduate course on numerical linear algebra with numerous applications to engineering and science. With a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions, this book is ideal for solving real-world problems. The text consists of six introductory chapters that thoroughly provide the required background for those who have not taken a course in applied or theoretical linear algebra. It explains in great detail the algorithms necessary for the accurate computation of the solution to the most frequently occurring problems in numerical linear algebra. In addition to examples from engineering and science applications, proofs of required results are provided without leaving out critical details. The Preface suggests ways in which the book can be used with or without an intensive study of proofs. This book will be a useful reference for graduate or advanced undergraduate students in engineering, science, and mathematics. It will also appeal to professionals in engineering and science, such as practicing engineers who want to see how numerical linear algebra problems can be solved using a programming language such as MATLAB, MAPLE, or Mathematica. - Six introductory chapters that thoroughly provide the required background for those who have not taken a course in applied or theoretical linear algebra - Detailed explanations and examples - A through discussion of the algorithms necessary for the accurate computation of the solution to the most frequently occurring problems in numerical linear algebra - Examples from engineering and science applications



Gaussian Integrals and their Applications

Author : Oscar A. Nieves

Publisher : CRC Press

Page : 83 pages

File Size : 35,92 MB

Release : 2024-07-30

Category : Mathematics

ISBN : 104010245X

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Book Description

Gaussian Integrals form an integral part of many subfields of applied mathematics and physics, especially in topics such as probability theory, statistics, statistical mechanics, quantum mechanics and so on. They are essential in computing quantities such as the statistical properties of normal random variables, solving partial differential equations involving diffusion processes, and gaining insight into the properties of particles. In Gaussian Integrals and their Applications, the author has condensed the material deemed essential for undergraduate and graduate students of physics and mathematics, such that for those who are very keen would know what to look for next if their appetite for knowledge remains unsatisfied by the time they finish reading this book. Features A concise and easily digestible treatment of the essentials of Gaussian Integrals Suitable for advanced undergraduates and graduate students in mathematics, physics, and statistics The only prerequisites are a strong understanding of multivariable calculus and linear algebra. Supplemented by numerous exercises (with fully worked solutions) at the end, which pertain to various levels of difficulty and are inspired by different fields in which Gaussian integrals are used.



Linear Algebra Tools For Data Mining (Second Edition)

Author : Dan A Simovici

Publisher : World Scientific

Page : 1002 pages

File Size : 47,9 MB

Release : 2023-06-16

Category : Computers

ISBN : 981127035X

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Book Description

This updated compendium provides the linear algebra background necessary to understand and develop linear algebra applications in data mining and machine learning.Basic knowledge and advanced new topics (spectral theory, singular values, decomposition techniques for matrices, tensors and multidimensional arrays) are presented together with several applications of linear algebra (k-means clustering, biplots, least square approximations, dimensionality reduction techniques, tensors and multidimensional arrays).The useful reference text includes more than 600 exercises and supplements, many with completed solutions and MATLAB applications.The volume benefits professionals, academics, researchers and graduate students in the fields of pattern recognition/image analysis, AI, machine learning and databases.



MATRIX AND LINEAR ALGEBRA AIDED WITH MATLAB, Third Edition

Author : Kanti Bhushan Datta

Publisher : PHI Learning Pvt. Ltd.

Page : 717 pages

File Size : 21,26 MB

Release : 2016-12-01

Category : Mathematics

ISBN : 8120352866

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Book Description

With the inclusion of applications of singular value decomposition (SVD) and principal component analysis (PCA) to image compression and data analysis, this edition provides a strong foundation of linear algebra needed for a higher study in signal processing. The use of MATLAB in the study of linear algebra for a variety of computational purposes and the programmes provided in this text are the most attractive features of this book which strikingly distinguishes it from the existing linear algebra books needed as pre-requisites for the study of engineering subjects. This book is highly suitable for undergraduate as well as postgraduate students of mathematics, statistics, and all engineering disciplines. The book will also be useful to Ph.D. students for relevant mathematical resources. NEW TO THIS EDITION The Third Edition of this book includes: • Simultaneous diagonalization of two diagonalizable matrices • Comprehensive exposition of SVD with applications in shear analysis in engineering • Polar Decomposition of a matrix • Numerical experimentation with a colour and a black-and-white image compression using MATLAB • PCA methods of data analysis and image compression with a list of MATLAB codes



Differential Equations and Linear Algebra

Author : Gilbert Strang

Publisher : Wellesley-Cambridge Press

Page : 0 pages

File Size : 15,39 MB

Release : 2015-02-12

Category : Mathematics

ISBN : 9780980232790

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Book Description

Differential equations and linear algebra are two central topics in the undergraduate mathematics curriculum. This innovative textbook allows the two subjects to be developed either separately or together, illuminating the connections between two fundamental topics, and giving increased flexibility to instructors. It can be used either as a semester-long course in differential equations, or as a one-year course in differential equations, linear algebra, and applications. Beginning with the basics of differential equations, it covers first and second order equations, graphical and numerical methods, and matrix equations. The book goes on to present the fundamentals of vector spaces, followed by eigenvalues and eigenvectors, positive definiteness, integral transform methods and applications to PDEs. The exposition illuminates the natural correspondence between solution methods for systems of equations in discrete and continuous settings. The topics draw on the physical sciences, engineering and economics, reflecting the author's distinguished career as an applied mathematician and expositor.