Matrix analysis for scientists and engineers.

*(English)*Zbl 1077.15001
Philadelphia, PA: SIAM (ISBN 0-89871-576-8/pbk). xiii, 157 p. (2005).

This book is a text for beginning graduate and senior level students in engineering and other sciences using matrix methods. In line with its purpose, it differs from linear algebra texts in two essential ways. Firstly, it is not an introductory text and thus assumes a basic knowledge of linear algebra, matrices and calculus as well as a certain amount of mathematical maturity. Secondly, linear algebra texts try to avoid the use of matrices as much as possible depending on the level aimed at. The subject of this book, however, is matrices, their properties and uses in applied mathematics. All the usual theorems of linear algebra are, of course, there, but the point of view is different. Moreover, the choice of topics is motivated both by applications and by computational utility and relevance.

The chapter headings are: 1. Introduction and review, 2. Vector spaces, 3. Linear transformations, 4. Introduction to the Moore-Penrose pseudoinverse, 5. Introduction to the singular value decomposition, 6. Linear equations, 7. Projections, inner product spaces and norms, 8. Linear least squares problems, 9. Eigenvalues and eigenvectors, 10. Canonical forms, 11. Linear differential and difference equations, 12. Generalized eigenvalue problems, 13. Kronecker products. There are exercises at the end of each chapter.

The author has taught the above material for many years and has found it to be very successful in preparing students from different backgrounds for their subsequent graduate studies in a variety of disciplines, in particular linear systems, signal processing, or estimation theory. This text can be used in a one-quarter or one-semester course and is also eminently suited for self-study. It is mathematically precise, rigorous and concise, and at the same time not heavy-going on account of the interspersed explanatory text, remarks and examples. It is, in fact, a pleasure to read and deserves to become a popular text among the students for whom it has been written.

The chapter headings are: 1. Introduction and review, 2. Vector spaces, 3. Linear transformations, 4. Introduction to the Moore-Penrose pseudoinverse, 5. Introduction to the singular value decomposition, 6. Linear equations, 7. Projections, inner product spaces and norms, 8. Linear least squares problems, 9. Eigenvalues and eigenvectors, 10. Canonical forms, 11. Linear differential and difference equations, 12. Generalized eigenvalue problems, 13. Kronecker products. There are exercises at the end of each chapter.

The author has taught the above material for many years and has found it to be very successful in preparing students from different backgrounds for their subsequent graduate studies in a variety of disciplines, in particular linear systems, signal processing, or estimation theory. This text can be used in a one-quarter or one-semester course and is also eminently suited for self-study. It is mathematically precise, rigorous and concise, and at the same time not heavy-going on account of the interspersed explanatory text, remarks and examples. It is, in fact, a pleasure to read and deserves to become a popular text among the students for whom it has been written.

Reviewer: Rabe von Randow (Bonn)

##### MSC:

15-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to linear algebra |

15A03 | Vector spaces, linear dependence, rank, lineability |

15A04 | Linear transformations, semilinear transformations |

15A09 | Theory of matrix inversion and generalized inverses |

15A06 | Linear equations (linear algebraic aspects) |

15A60 | Norms of matrices, numerical range, applications of functional analysis to matrix theory |

15A63 | Quadratic and bilinear forms, inner products |

15A18 | Eigenvalues, singular values, and eigenvectors |

15A21 | Canonical forms, reductions, classification |

34A30 | Linear ordinary differential equations and systems |

39A10 | Additive difference equations |

15A69 | Multilinear algebra, tensor calculus |