Linear algebra permeates mathematics, perhaps more so than any other single subject. It plays an essential role in pure and applied mathematics, statistics, computer science, and many aspects of physics and engineering. This book conveys in a user-friendly way the basic and advanced techniques of linear algebra from the point of view of a working analyst. The techniques are illustrated by a wide sample of applications and examples that are chosen to highlight the tools of the trade. In short, this is material that the author wishes he had been taught as a graduate student.
Roughly the first third of the book covers the basic material of a first course in linear algebra. The remaining chapters are devoted to applications drawn from vector calculus, numerical analysis, control theory, complex analysis, convexity and functional analysis. In particular, fixed point theorems, extremal problems, matrix equations, zero location and eigenvalue location problems, and matrices with nonnegative entries are discussed. Appendices on useful facts from analysis and supplementary information from complex function theory are also provided for the convenience of the reader.
The book is suitable as a text or supplementary reference for a variety of courses on linear algebra and its applications, as well as for self-study.
Harry Dym, Weizmann Institute of Science, Rehovot, Israel.
* Vector spaces * Gaussian elimination * Additional applications of Gaussian elimination * Eigenvalues and eigenvectors * Determinants * Calculating Jordan forms * Normed linear spaces * Inner product spaces and orthogonality * Symmetric, Hermitian and normal matrices * Singular values and related inequalities * Pseudoinverses * Triangular factorization and positive definite matrices * Difference equations and differential equations * Vector valued functions * The implicit function theorem * Extremal problems * Matrix valued holomorphic functions * Matrix equations * Realization theory * Eigenvalue location problems * Zero location problems * Convexity Matrices with nonnegative entries * Some facts from analysis * More complex variables * Bibliography * Notation * Index * Subject index