Multilinear Algebra

D. G. Northcott

doi:10.1017/CBO9780511565939

Multilinear algebra has important applications in many different areas of mathematics but is usually learned in a rather haphazard fashion. The aim of this book is to provide a readable and systematic account of multilinear algebra at a level suitable for graduate students. Professor Northcott gives a thorough treatment of topics such as tensor, exterior, Grassmann, Hopf and co-algebras and ends each chapter with a section entitled 'Comments and Exercises'. The comments contain convenient summaries and discussion of the content whilst the exercises provide an opportunity to test understanding and add extra material. Complete solutions are provided for those exercises that are particularly important or used later in the book. The volume as a whole is based on advanced lectures given by the author at the University of Sheffield.

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Multilinear Algebra

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Contents

Frontmatter
pp i-iv

Contents
pp v-viii

Preface
pp ix-x

1 - Multilinear mappings
pp 1-18

2 - Some properties of tensor products
pp 19-41

3 - Associative algebras
pp 42-68

4 - The tensor algebra of a module
pp 69-83

5 - The exterior algebra of a module
pp 84-116

6 - The symmetric algebra of a module
pp 117-129

7 - Coalgebras and Hopf algebras
pp 130-174

8 - Graded duality
pp 175-196

Index
pp 197-198

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Multilinear Algebra

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