"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) ***************************************************************************** "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.