Linear Algebra

1. Front Matter

   Pages II-XI

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2. Linear spaces

   • Werner H. Greub

   Pages 1-15

3. Linear transformations

   • Werner H. Greub

   Pages 16-31

4. Matrices

   • Werner H. Greub

   Pages 31-46

5. Determinants

   • Werner H. Greub

   Pages 46-71

6. Oriented linear spaces

   • Werner H. Greub

   Pages 71-81

7. Multilinear mappings

   • Werner H. Greub

   Pages 81-95

8. Tensor-Algebra

   • Werner H. Greub

   Pages 96-111

9. Exterior Algebra

   • Werner H. Greub

   Pages 112-133

10. Duality in exterior algebra

    • Werner H. Greub

    Pages 133-160

11. Inner product spaces

    • Werner H. Greub

    Pages 160-185

12. Linear mappings of inner product spaces

    • Werner H. Greub

    Pages 186-220

13. Symmetric bilinear functions

    • Werner H. Greub

    Pages 220-250

14. Quadrics

    • Werner H. Greub

    Pages 250-275

15. Unitary Spaces

    • Werner H. Greub

    Pages 275-302

16. Invariant subspaces

    • Werner H. Greub

    Pages 302-333

17. Back Matter

    Pages 333-338

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Besides the very obvious change from German to English, the second edition of this book contains many additions as weil as a great many other changes. It might even be called a new book altogether were it not for the fact that the essential character of the book has remained the same; in other words, the entire presentation continues to be based on an axiomatic treatment of linear spaces. In this second edition, the thorough-going restriction to linear spaces of finite dimension has been removed. Another complete change is the restriction to linear spaces with real or complex coefficients, thereby removing a number of relatively involved discussions which did not really contribute substantially to the subject. On p.6 there is a list of those chapters in which the presentation can be transferred directly to spaces over an arbitrary coefficient field. Chapter I deals with the general properties of a linear space. Those concepts which are only valid for finitely many dimensions are discussed in a special paragraph. Chapter 11 now covers only linear transformations while the treat­ ment of matrices has been delegated to a new chapter, chapter 111. The discussion of dual spaces has been changed; dual spaces are now intro­ duced abstractly and the connection with the space of linear functions is not established untillater.

• algebra
• field
• linear algebra
• matrices
• transformation

• Mathematics Department, University of Toronto, Canada

  Werner H. Greub

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