Fundamentals of Matrix Analysis with Applications

Fundamentals of Matrix Analysis with Applications PDF

Author: Edward Barry Saff

Publisher: John Wiley & Sons

Published: 2015-10-12

Total Pages: 407

ISBN-13: 111895369X

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An accessible and clear introduction to linear algebra with a focus on matrices and engineering applications Providing comprehensive coverage of matrix theory from a geometric and physical perspective, Fundamentals of Matrix Analysis with Applications describes the functionality of matrices and their ability to quantify and analyze many practical applications. Written by a highly qualified author team, the book presents tools for matrix analysis and is illustrated with extensive examples and software implementations. Beginning with a detailed exposition and review of the Gauss elimination method, the authors maintain readers’ interest with refreshing discussions regarding the issues of operation counts, computer speed and precision, complex arithmetic formulations, parameterization of solutions, and the logical traps that dictate strict adherence to Gauss’s instructions. The book heralds matrix formulation both as notational shorthand and as a quantifier of physical operations such as rotations, projections, reflections, and the Gauss reductions. Inverses and eigenvectors are visualized first in an operator context before being addressed computationally. Least squares theory is expounded in all its manifestations including optimization, orthogonality, computational accuracy, and even function theory. Fundamentals of Matrix Analysis with Applications also features: Novel approaches employed to explicate the QR, singular value, Schur, and Jordan decompositions and their applications Coverage of the role of the matrix exponential in the solution of linear systems of differential equations with constant coefficients Chapter-by-chapter summaries, review problems, technical writing exercises, select solutions, and group projects to aid comprehension of the presented concepts Fundamentals of Matrix Analysis with Applications is an excellent textbook for undergraduate courses in linear algebra and matrix theory for students majoring in mathematics, engineering, and science. The book is also an accessible go-to reference for readers seeking clarification of the fine points of kinematics, circuit theory, control theory, computational statistics, and numerical algorithms.

Fundamentals of Matrix Analysis with Applications Set

Fundamentals of Matrix Analysis with Applications Set PDF

Author: Edward Barry Saff

Publisher: John Wiley & Sons

Published: 2016-02-08

Total Pages: 0

ISBN-13:

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This set includes Fundamentals of Matrix Analysis with Applications & Solutions Manual to Accompany Fundamentals of Matrix Analysis with Applications Providing comprehensive coverage of matrix theory from a geometric and physical perspective, Fundamentals of Matrix Analysis with Applications describes the functionality of matrices and their ability to quantify and analyze many practical applications. Written by a highly qualified author team, the book presents tools for matrix analysis and is illustrated with extensive examples and software implementations. Beginning with a detailed exposition and review of the Gauss elimination method, the authors maintain readers’ interest with refreshing discussions regarding the issues of operation counts, computer speed and precision, complex arithmetic formulations, parameterization of solutions, and the logical traps that dictate strict adherence to Gauss’s instructions. The book heralds matrix formulation both as notational shorthand and as a quantifier of physical operations such as rotations, projections, reflections, and the Gauss reductions. Inverses and eigenvectors are visualized first in an operator context before being addressed computationally. Least squares theory is expounded in all its manifestations including optimization, orthogonality, computational accuracy, and even function theory. Fundamentals of Matrix Analysis with Applications also features: Novel approaches employed to explicate the QR, singular value, Schur, and Jordan decompositions and their applications Coverage of the role of the matrix exponential in the solution of linear systems of differential equations with constant coefficients Chapter-by-chapter summaries, review problems, technical writing exercises, select solutions, and group projects to aid comprehension of the presented concepts

Matrix Analysis for Statistics

Matrix Analysis for Statistics PDF

Author: James R. Schott

Publisher: John Wiley & Sons

Published: 2016-05-31

Total Pages: 698

ISBN-13: 1119092469

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An up-to-date version of the complete, self-contained introduction to matrix analysis theory and practice Providing accessible and in-depth coverage of the most common matrix methods now used in statistical applications, Matrix Analysis for Statistics, Third Edition features an easy-to-follow theorem/proof format. Featuring smooth transitions between topical coverage, the author carefully justifies the step-by-step process of the most common matrix methods now used in statistical applications, including eigenvalues and eigenvectors; the Moore-Penrose inverse; matrix differentiation; and the distribution of quadratic forms. An ideal introduction to matrix analysis theory and practice, Matrix Analysis for Statistics, Third Edition features: • New chapter or section coverage on inequalities, oblique projections, and antieigenvalues and antieigenvectors • Additional problems and chapter-end practice exercises at the end of each chapter • Extensive examples that are familiar and easy to understand • Self-contained chapters for flexibility in topic choice • Applications of matrix methods in least squares regression and the analyses of mean vectors and covariance matrices Matrix Analysis for Statistics, Third Edition is an ideal textbook for upper-undergraduate and graduate-level courses on matrix methods, multivariate analysis, and linear models. The book is also an excellent reference for research professionals in applied statistics. James R. Schott, PhD, is Professor in the Department of Statistics at the University of Central Florida. He has published numerous journal articles in the area of multivariate analysis. Dr. Schott’s research interests include multivariate analysis, analysis of covariance and correlation matrices, and dimensionality reduction techniques.

Matrix Analysis and Applied Linear Algebra, Second Edition

Matrix Analysis and Applied Linear Algebra, Second Edition PDF

Author: Carl D. Meyer

Publisher: SIAM

Published: 2023-05-18

Total Pages: 257

ISBN-13: 1611977460

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This second edition has been almost completely rewritten to create a textbook designed to provide flexibility for nearly any desired degree of rigor and depth of coverage. This is achieved with a linear development ensuring that material at any point is not dependent on subsequent developments and by means of graduated levels of sophistication. The text moves from traditional first principles in early chapters to deeper topics involving both theory and applications in later chapters. This allows for a traditional single-term course based on roughly half of the text without having to refer to more advanced topics while the later portion of the book facilitates a seamless two-term course covering the range of theory and applications generally reserved for discussions beyond fundamentals. Rigor is present throughout, but the level is adaptable because all major theorems have ample accompanying discussions and illustrative examples designed to convince readers and students of the validity of a result without a deep dive into the proof. Moreover, there is an expanded emphasis on both the depth and breadth of applications that are designed to illuminate the utility of the subject across broad areas of science and engineering. At major junctures there are photos and historical remarks concerning the personalities who created and contributed to the subject’s development. Throughout there are carefully constructed exercises ranging from easy to moderately challenging to difficult, many of which condition students for topics that follow.

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