About the Book
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.
About the Author :
Edward Barry Saff, PhD, is Professor in the Department of Mathematics and Director of the Center for Constructive Approximation at Vanderbilt University. Dr. Saff is an Inaugural Fellow of the American Mathematical Society, Foreign Member of the Bulgarian Academy of Science, and the recipient of both a Guggenheim and Fulbright Fellowship. He is Editor-in-Chief of two research journals, Constructive Approximation and Computational Methods and Function Theory, and has authored or co-authored over 250 journal articles and eight books. Dr. Saff also serves as an organizer for a sequence of international research conferences that help to foster the careers of mathematicians from developing countries.
Arthur David Snider, PhD, is Professor Emeritus at the University of South Florida (USF), where he served on the faculties of the Departments of Mathematics, Physics, and Electrical Engineering. Previously an analyst at the Massachusetts Institute of Technology's Draper Lab and recipient of the USF Krivanek Distinguished Teacher Award, he consults in industry and has authored or co-authored over 100 journal articles and eight books. With the support of National Science Foundation, Dr. Snider also pioneered a course in fine art appreciation for engineers.
Review :
Providing comprehensive coverage of matrix theory from a geometric and physical perspective, the book 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. (Zentralblatt MATH 2016)
This is a straightforward modern introduction to matrices..... a very well done text, probably most suitable for engineering students. (Mathematical Association of America 2016)
This is a straightforward modern introduction to matrices. As the title indicates, the emphasis is on the tool of matrices rather than the theory of linear spaces. There is a moderate amount on linear spaces, but this is oriented toward supporting some of the more advanced matrix operations rather than as a subject in itself.
The book starts out with a very detailed, almost loving, exposition of Gaussian elimination, and parlays that into the formalism of matrix algebra. Most of the rest of the book deals with useful matrix operations, and in particular with particular forms and decompositions of matrices, such as diagonalization through eigenvectors, LU and QR factorizations, Schur and Jordan forms, and SVD (singular value decomposition). At the end of each of the three sections of the book are several longer projects with realistic applications, mostly from electrical engineering with some mechanics and control theory. These a billed as group projects, but could just as well be individual projects. The last third of the book deals with differential equations, using these as an opportunity to introduce even more matrix techniques. There's no companion web site for this book.
The book has copious exercises; most are numeric drill, with a few generalizations and simple proofs. Many of these are flagged to be done with a calculator or a computer and to examine the round-off errors. There are also a few "technical writing exercises" in each of the three sections; these ask the student to investigate something and write an explanation in words. There's not any guidance on these in the text, so I think the instructor would have to give a lot of coaching to get anything useful. These are short exercises and would probably generate 1- to 2-page papers.
There are answers to the odd-numbered problems in the back. There is also a solutions manual for this book from the same authors and the same publisher. This has concise, complete solutions for all problems in the text. This manual is sold openly to anyone (on Amazon, for example) and is not one of those that is available only to instructors.
Very Good Feature: lots of examples using SVD.
Very Good Feature: the computational aspects are well-integrated into the narrative. (There is one silly statement about computers, though. On p. 95, in talking about the advantages of doing Gaussian elimination on a determinant rather than using Cramer's rule, the book says, "So using elementary row operations the Tianhe-2 could calculate a 25-by-25 determinant in a fraction of a picosecond." In truth, any current computer takes around a nanosecond (10-9
second) per operation, so doing anything in a picosecond (10^-12}
second) is impossible. The misapprehension comes because the Tianhe-2 is a massively parallel computer with over 3 million cores and an advertised top speed of 33.86 petaflops. Because of the parallelism, if all the cores are busy the average time per operation across the whole computer is under a picosecond, but no individual operation is anywhere near that fast.)
Bottom line: a very well done text, probably most suitable for engineering students. Math students would be better served by a book that combines matrices with a more thorough coverage of linear spaces; I like Strang's Introduction to Linear Algebra. (Allen Stenger)
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This book provides comprehensive coverage of matrix theory from a geometric and physical perspective, and the authors address the functionality of matrices and their ability to illustrate and aid in many practical applications. Readers are introduced to inverses and eigenvalues through physical examples such as rotations, reflections, and projections, and only then are computational details described and explored. (http: //cds.cern.ch/record/2050353)
Providing comprehensive coverage of matrix theory from a geometric and physical perspective, the book describes the functionality of matrices and their ability to quantify and analyze many practical applications. Written by a highly qualied author team, the book presents tools for matrix analysis and is illustrated with extensive examples and software implementations.
