About this book Introduction This book is built around the material on multilinear algebra which in chapters VI to IX of the second edition of Linear Algebra was included but exc1uded from the third edition. It is designed to be a sequel and companion volume to the third edition of Linear Algebra. In fact, the terminology and basic results of that book are frequently used without reference. In particular, the reader should be familiar with chapters I to V and the first part of chapter VI although other sections are occasionally used.

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In particular, the reader should be familiar with Chapters and the first part of Chapter 6 of that book, although other sections are occasionally used. In this new version of Multilinear Algebra, Chapters remain essen tially unchanged from the previous edition. Chapter 6 has been completely rewritten and split into three Chapters 6, 7, and 8.

Some of the proofs have been simplified and a substantial amount of new material has been added. This applies particularly to the study of characteristic coefficients and the Pfaffian. The old Chapter 7 remains as it stood, except that it is now Chapter 9. The old Chapter 8 has been suppressed and the material which it con tained multilinear functions has been relocated at the end of Chapters 3, 5, and 9. The last two chapters on Clifford algebras and their representations are completely new.

In view of the growing importance of Clifford algebras and the relatively few references available, it was felt that these chapters would be useful to both mathematicians and physicists. Read more.

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## Multilinear Algebra

It is designed to be a sequel and companion volume to the third edition of Linear Algebra. In fact, the terminology and basic results of that book are frequently used without reference. In particular, the reader should be familiar with chapters I to V and the first part of chapter VI although other sections are occasionally used. The essential difference between the present treatment and that of the second edition lies in the full exploitation of universal properties which eliminates the restrietion to vector spaces of finite dimension. Chapter I contains standard material on multilinear mappings and the tensor product of vector spaces. The fundamental concept of "tensor product" is used in Chapter to construct the tensor algebra over a given vector space.

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Werner Greub This book is a revised version of the first edition and is intended as a sequel and companion volume to the fourth edition of Linear Algebra Graduate Texts in Mathematics As before, the terminology and basic results of Linear Algebra are frequently used without reference. In particular, the reader should be familiar with Chapters and the first part of Chapter 6 of that book, although other sections are occasionally used. In this new version of Multilinear Algebra, Chapters remain essentially unchanged from the previous edition. Chapter 6 has been completely rewritten and split into three Chapters 6, 7, and 8. Some of the proofs have been simplified and a substantial amount of new material has been added.

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The final prices may differ from the prices shown due to specifics of VAT rules About this Textbook This book is a revised version of the first edition and is intended as a Linear Algebra sequel and companion volume to the fourth edition of Graduate Texts in Mathematics In particular, the reader should be familiar with Chapters and the first part of Chapter 6 of that book, although other sections are occasionally used. Chapter 6 has been completely rewritten and split into three Chapters 6, 7, and 8. Some of the proofs have been simplified and a substantial amount of new material has been added. This applies particularly to the study of characteristic coefficients and the Pfaffian. The old Chapter 7 remains as it stood, except that it is now Chapter 9. The last two chapters on Clifford algebras and their representations are completely new.

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