This textbook for senior undergraduate and first year graduate-level courses in linear algebra and analysis, covers linear algebra, multilinear algebra, canonical forms of matrices, normal linear vector spaces and inner product spaces. These topics provide all of the prerequisites for graduate students in mathematics to prepare for advanced-level work in such areas as algebra, analysis, topology and applied mathematics.
Author(s): William C. Brown
Publisher: Wiley-Interscience
Year: 1988
Language: English
Pages: 277
Front Cover......Page 1
Title Page......Page 4
Copyright Information......Page 5
Dedication......Page 6
Preface......Page 8
Contents......Page 10
1. Definitions and Examples of Vector Spaces......Page 14
2. Bases and Dimension......Page 21
3. Linear Transformations......Page 30
4. Products and Direct Sums......Page 43
5. Quotient Spaces and the Isomorphism Theorems......Page 51
6. Duals and Adjoints......Page 59
7. Symmetric Bilinear Forms......Page 66
1. Multilinear Maps and Tensor Products......Page 72
2. Functorial Properties of Tensor Products......Page 81
3. Alternating Maps and Exterior Powers......Page 96
4. Symmetric Maps and Symmetric Powers......Page 107
1. Preliminaries on Fields......Page 111
2. Minimal and Characteristic Polynomials......Page 118
3. Eigenvalues and Eigenvectors......Page 130
4. The Jordan Canonical Form......Page 145
5. The Real Jordan Canonical Form......Page 154
6. The Rational Canonical Form......Page 172
1. Basic Definitions and Examples......Page 184
2. Product Norms and Equivalence......Page 193
3. Sequential Compactness and the Equivalence of Norms......Page 199
4. Banach Spaces......Page 213
1. Real Inner Product Spaces......Page 219
2. Self-adjoint Transformations......Page 234
3. Complex Inner Product Spaces......Page 249
4. Normal Operators......Page 256
Glossary of Notation......Page 267
References......Page 272
Subject Index......Page 274
