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Advanced Linear Algebra

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Author(s): Steven Roman (auth.)
Series: Graduate Texts in Mathematics 135
Edition: 3rd ed
Publisher: Springer New York
Year: 1992

Language: English
Pages: 541
City: New York
Tags: Linear and Multilinear Algebras, Matrix Theory

Front Matter....Pages i-xii
Preliminaries....Pages 1-24
Front Matter....Pages 25-25
Vector Spaces....Pages 27-43
Linear Transformations....Pages 45-62
The Isomorphism Theorems....Pages 63-81
Modules I....Pages 83-95
Modules II....Pages 97-106
Modules over Principal Ideal Domains....Pages 107-119
The Structure of a Linear Operator....Pages 121-133
Eigenvalues and Eigenvectors....Pages 135-156
Real and Complex Inner Product Spaces....Pages 157-174
The Spectral Theorem for Normal Operators....Pages 175-202
Front Matter....Pages 203-203
Metric Vector Spaces....Pages 205-237
Metric Spaces....Pages 239-261
Hilbert Spaces....Pages 263-290
Tensor Products....Pages 291-314
Affine Geometry....Pages 315-328
The Umbral Calculus....Pages 329-352
Back Matter....Pages 353-366