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.

This IMA Volume in Mathematics and its Applications COMBINATORIAL AND GRAPH-THEORETICAL PROBLEMS IN LINEAR ALGEBRA is based on the proceedings of a workshop that was an integral part of the 1991-92 IMA program on "Applied Linear Algebra." We are grateful to Richard Brualdi, George Cybenko, Alan George, Gene Golub, Mitchell Luskin, and Paul Van Dooren for planning and implementing the year-long program. We especially thank Richard Brualdi, Shmuel Friedland, and Victor Klee for organizing this workshop and editing the proceedings. The financial support of the National Science Foundation made the workshop possible. A vner Friedman Willard Miller, Jr. PREFACE The 1991-1992 program of the Institute for Mathematics and its Applications (IMA) was Applied Linear Algebra. As part of this program, a workshop on Com binatorial and Graph-theoretical Problems in Linear Algebra was held on November 11-15, 1991. The purpose of the workshop was to bring together in an informal setting the diverse group of people who work on problems in linear algebra and matrix theory in which combinatorial or graph theoretic analysis is a major com ponent. Many of the participants of the workshop enjoyed the hospitality of the IMA for the entire fall quarter, in which the emphasis was discrete matrix analysis."