Multilinear Algebra: 1st Edition (Hardback) book cover

Multilinear Algebra

1st Edition

By Russell Merris

CRC Press

340 pages

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Hardback: 9789056990787
pub: 1997-08-20
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The prototypical multilinear operation is multiplication. Indeed, every multilinear mapping can be factored through a tensor product. Apart from its intrinsic interest, the tensor product is of fundamental importance in a variety of disciplines, ranging from matrix inequalities and group representation theory, to the combinatorics of symmetric functions, and all these subjects appear in this book. Another attraction of multilinear algebra lies in its power to unify such seemingly diverse topics. This is done in the final chapter by means of the rational representations of the full linear group. Arising as characters of these representations, the classical Schur polynomials are one of the keys to unification. Prerequisites for the book are minimized by self-contained introductions in the early chapters. Throughout the text, some of the easier proofs are left to the exercises, and some of the more difficult ones to the references.

Table of Contents

1. Partitions 2. Inner Product Spaces 3. Permutation Groups 4. Tensor Spaces 5. Symmetry Classes of Tensors 6. Generalized Matrix Functions 7. Group Representation Theory 8. The Rational Representations of GL(n,C)

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Algebra, Logic and Applications

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Algebra / General