Ebook: Linear Algebra

This textbook gives a detailed and comprehensive presentation of linear algebra based on an axiomatic treatment of linear spaces. For this fourth edition some new material has been added to the text, for instance, the intrinsic treatment of the classical adjoint of a linear transformation in Chapter IV, as well as the discussion of quaternions and the classifica­ tion of associative division algebras in Chapter VII. Chapters XII and XIII have been substantially rewritten for the sake of clarity, but the contents remain basically the same as before. Finally, a number of problems covering new topics-e.g. complex structures, Caylay numbers and symplectic spaces - have been added. I should like to thank Mr. M. L. Johnson who made many useful suggestions for the problems in the third edition. I am also grateful to my colleague S. Halperin who assisted in the revision of Chapters XII and XIII and to Mr. F. Gomez who helped to prepare the subject index. Finally, I have to express my deep gratitude to my colleague J. R. Van­ stone who worked closely with me in the preparation of all the revisions and additions and who generously helped with the proof reading.

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This textbook gives a detailed and comprehensive presentation of the linear algebra based on axiomatic treatment of linear spaces. The author maintains a good balance between modern algebraic interests and traditional linear algebra. Several chapters have been substantially rewritten for clarity of exposition, although their basic content is unchanged. A considerable number of exer- cises covering new material has also been added.

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This textbook gives a detailed and comprehensive presentation of the linear algebra based on axiomatic treatment of linear spaces. The author maintains a good balance between modern algebraic interests and traditional linear algebra. Several chapters have been substantially rewritten for clarity of exposition, although their basic content is unchanged. A considerable number of exer- cises covering new material has also been added.
Content:
Front Matter....Pages I-XVII
Prerequisites....Pages 1-4
Vector Spaces....Pages 5-40
Linear Mappings....Pages 41-82
Matrices....Pages 83-98
Determinants....Pages 99-143
Algebras....Pages 144-166
Gradations and homology....Pages 167-185
Inner product spaces....Pages 186-215
Linear mappings of inner product spaces....Pages 216-260
Symmetric bilinear functions....Pages 261-295
Quadrics....Pages 296-324
Unitary spaces....Pages 325-350
Polynomial Algebras....Pages 351-382
Theory of a linear transformation....Pages 383-444
Back Matter....Pages 445-451

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This textbook gives a detailed and comprehensive presentation of the linear algebra based on axiomatic treatment of linear spaces. The author maintains a good balance between modern algebraic interests and traditional linear algebra. Several chapters have been substantially rewritten for clarity of exposition, although their basic content is unchanged. A considerable number of exer- cises covering new material has also been added.
Content:
Front Matter....Pages I-XVII
Prerequisites....Pages 1-4
Vector Spaces....Pages 5-40
Linear Mappings....Pages 41-82
Matrices....Pages 83-98
Determinants....Pages 99-143
Algebras....Pages 144-166
Gradations and homology....Pages 167-185
Inner product spaces....Pages 186-215
Linear mappings of inner product spaces....Pages 216-260
Symmetric bilinear functions....Pages 261-295
Quadrics....Pages 296-324
Unitary spaces....Pages 325-350
Polynomial Algebras....Pages 351-382
Theory of a linear transformation....Pages 383-444
Back Matter....Pages 445-451
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