Multilinear Algebra, Gordon & Breach, Amsterdam, 1997

ISBN 90-5699-078-0. Math. Reviews 98i:15002. Available from Barnes & Noble and Amazon.com.

Ideally suited for a fourth year undergraduate "capstone" course, Multilinear Algebra is also an attractive choice for a beginning graduate course and/or as a research reference. The first four chapters consist of self-contained introductions to those prerequisite notions beyond the standard third year undergraduate courses in abstract and linear algebra.

Apart from applications to graph theory and the "excursion" into Invariant Theory, the use of Schur functions as a unifying vehicle in the final chapter may be of particular interest to combinatorialists.

Contents

1. Partitions (with Applications to Graphs)

2. Inner Product Spaces (with Applications to Graphs)

3. Permutation Groups (with Applications to Symmetry)

4. Group Representation Theory

5. Tensor Spaces

6. Symmetry Classes of Tensors (with Applications to the Theory of Enumeration)

7. Generalized Matrix Functions (with an Excursion into Invariant Theory)

8. The Rational Representations of GL(n,C) (with Applications to Graphs)

Please E-mail errata suggestions to the author: merris@csuhayward.edu

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