Matrix Theory

Designed for a second-semester course in linear algebra, this classroom-tested text creates a bridge from linear algebra concepts to more advanced abstract algebra and matrix theory. It focuses on the development of the Moore-Penrose inverse and uses concrete examples to make arguments clear. The authors provide MATLAB® examples and exercises throughout as well as numerous homework problems and suggestions for further reading. The appendices present basic linear algebra topics and related prerequisites. Delving into elementary linear algebra ideas at a deeper level, this book prepares readers for further study in matrix theory and abstract algebra.

In 1990, the National Science Foundation recommended that every college mathematics curriculum should include a second course in linear algebra. In answer to this recommendation, Matrix Theory: From Generalized Inverses to Jordan Form provides the material for a second semester of linear algebra that probes introductory linear algebra concepts while also exploring topics not typically covered in a sophomore-level class.

Tailoring the material to advanced undergraduate and beginning graduate students, the authors offer instructors flexibility in choosing topics from the book. The text first focuses on the central problem of linear algebra: solving systems of linear equations. It then discusses LU factorization, derives Sylvester's rank formula, introduces full-rank factorization, and describes generalized inverses. After discussions on norms, QR factorization, and orthogonality, the authors prove the important spectral theorem. They also highlight the primary decomposition theorem, Schur's triangularization theorem, singular value decomposition, and the Jordan canonical form theorem. The book concludes with a chapter on multilinear algebra.

With this classroom-tested text students can delve into elementary linear algebra ideas at a deeper level and prepare for further study in matrix theory and abstract algebra.

Each chapter ends with a list of references for further reading. Undoubtedly, these will be useful for anyone who wishes to pursue the topics deeper. the book has many MATLAB examples and problems presented at appropriate places. the book will become a widely used classroom text for a second course on linear algebra. It can be used profitably by graduate and advanced level undergraduate students. It can also serve as an intermediate course for more advanced texts in matrix theory. This is a lucidly written book by two authors who have made many contributions to linear and multilinear algebra.K.C. Sivakumar, IMAGE, No. 47, Fall 2011 Always mathematically constructive, this book helps readers delve into elementary linear algebra ideas at a deeper level and prepare for further study in matrix theory and abstract algebra.L'enseignement Mathématique, January-June 2007, Vol. 53, No. 1-2

Autorentext

Piziak, Robert; Odell, P.L.

Inhalt

The Idea of Inverse. Generating Invertible Matrices. Subspaces Associated to Matrices. The Moore Penrose Inverse. Generalized Inverses. Norms. Inner Products. Projections. Spectral Theory. Matrix Diagonalization. The Jordan Canonical Form. Multilinear Matters.