Matrices

Algebra, Analysis and Applications

This volume deals with advanced topics in matrix theory using the notions and tools from algebra, analysis, geometry and numerical analysis. It consists of seven chapters that are loosely connected and interdependent. The choice of the topics is very personal and reflects the subjects that the author was actively working on in the last 40 years. Many results appear for the first time in the volume. Readers will encounter various properties of matrices with entries in integral domains, canonical forms for similarity, and notions of analytic, pointwise and rational similarity of matrices with entries which are locally analytic functions in one variable. This volume is also devoted to various properties of operators in inner product space, with tensor products and other concepts in multilinear algebra, and the theory of non-negative matrices. It will be of great use to graduate students and researchers working in pure and applied mathematics, bioinformatics, computer science, engineering, operations research, physics and statistics.

Contents:

• Domains, Modules and Matrices
• Canonical Forms for Similarity
• Functions of Matrices and Analytic Similarity
• Inner Product Spaces
• Elements of Multilinear Algebra
• Non-Negative Matrices
• Various Topics

Readership: Graduate students, researchers in mathematics, applied mathematics, statistics, computer science, bioinformatics, engineering, and physics.
Key Features:

• Includes a number of selected related topics in matrix theory that the author was actively working on for 40 years
• Includes many results that are not available in the books that are currently on the market