A Second Course in Linear Algebra

✍ Scribed by William C. Brown

• Publisher: Wiley-Interscience
• Year: 1988
• Tongue: English
• Leaves: 277
• Category: Library

✦ Synopsis

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.
Presents a formal approach to advanced topics in linear algebra, the mathematics being presented primarily by means of theorems and proofs. Covers multilinear algebra, including tensor products and their functorial properties. Discusses minimal and characteristic polynomials, eigenvalues and eigenvectors, canonical forms of matrices, including the Jordan, real Jordan, and rational canonical forms. Covers normed linear vector spaces, including Banach spaces. Discusses product spaces, covering real inner product spaces, self-adjoint transformations, complex inner product spaces, and normal operators.

✦ Table of Contents

Cover......Page 1
S Title......Page 2
A Second Course in Linear Algebra......Page 4
QA184.B765 1987 517.5......Page 5
Dedicated To Linda......Page 6
Preface......Page 8
Contents......Page 10
1. DEFINITIONS AND EXAMPLES OF VECTOR SPACES......Page 14
EXERCISES FOR SECTION 1......Page 19
2. BASES AND DIMENSION......Page 21
EXERCISES FOR SECTION 2......Page 28
3. LINEAR TRANSFORMATIONS......Page 30
EXERCISES FOR SECTION 3......Page 41
4. PRODUCTS AND DIRECT SUMS......Page 43
EXERCISES FOR SECTION 4......Page 50
5. QUOTIENT SPACES AND THE ISOMORPHISM THEOREMS......Page 51
EXERCISES FOR SECTION 5......Page 57
6. DUALS AND ADJOINTS......Page 59
EXERCISES FOR SECTION 6......Page 64
7. SYMMETRIC BILINEAR FORMS......Page 66
EXERCISES FOR SECTION 7......Page 70
1. MULTILINEAR MAPS AND TENSOR PRODUCTS......Page 72
EXERCISES FOR SECTION 1......Page 80
2. FUNCTORIAL PROPERTIES OF TENSOR PRODUCTS......Page 81
EXERCISES FOR SECTION 2......Page 94
3. ALTERNATING MAPS AND EXTERIOR POWERS......Page 96
EXERCISES FOR SECTION 3......Page 106
4. SYMMETRIC MAPS AND SYMMETRIC POWERS......Page 107
EXERCISES FOR SECTION 4......Page 109
1. PRELIMINARIES ON FIELDS......Page 111
EXERCISES FOR SECTION 1......Page 116
2. MINIMAL AND CHARACTERISTIC POLYNOMIALS......Page 118
EXERCISES FOR SECTION 2......Page 128
3. EUGENVALUES AND EIGENVECTORS......Page 130
EXERCISES FOR SECTION 3......Page 143
4. THE JORDAN CANONICAL FORM......Page 145
EXERCISES FOR SECTION 4......Page 153
5. THE REAL JORDAN CANONICAL FORM......Page 154
EXERCISES FOR SECTION 5......Page 170
6. THE RATIONAL CANONICAL FORM......Page 172
EXERCISES FOR SECTION 6......Page 181
1. BASiC DEFINITIONS AND EXAMPLES......Page 184
EXERCISES FOR SECTION 1......Page 191
2. PRODUCT NORMS AND EQUIVALENCE......Page 193
EXERCiSES FOR SECTION 2......Page 197
3. SEQUENTIAL COMPACTNESS AND THE EQUIVALENCE OF NORMS......Page 199
EXERCISES FOR SECTION 3......Page 211
4. BANACH SPACES......Page 213
EXERCISES FOR SECTION 4......Page 217
1. REAL INNER PRODUCT SPACES......Page 219
EXERCISES FOR SECTION 1......Page 233
2. SELF-ADJOINT TRANSFORMATIONS......Page 234
EXERCiSES FOR SECTION 2......Page 247
3. COMPLEX INNER PRODUCT SPACES......Page 249
EXERCISES FOR SECTION 3......Page 255
4. NORMAL OPERATORS......Page 256
EXERCISES FOR SECTION 4......Page 265
Glossary of Notation......Page 267
References......Page 272
Subject Index......Page 274