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Tables of Contents for Linear Algebra
Chapter/Section Title
Page #
Page Count
Preface
ix
 
Algebraic Preamble
1
12
Groups, Rings and Fields
1
5
Permutation Groups
6
3
Problems 1
9
4
Vector Spaces and Linear Maps
13
26
Vector Spaces and Algebras
13
4
Bases and Dimension
17
5
Linear Maps
22
6
Direct Sums
28
4
Addendum -- Modules
32
1
Problems 2
33
6
Matrices, Determinants and Linear Equations
39
36
Matrices
39
12
Determinants
51
11
Systems of Linear Equations
62
5
Problems 3
67
8
Cayley--Hamilton Theorem and Jordan Form
75
34
Polynomials
75
6
Cayley-Hamilton and Spectral Theorems
81
11
Jordan Form
92
11
Problems 4
103
6
Interlude on Finite Fields
109
16
Finite Fields
109
7
Applications-Linear Codes and Finite Matrix Groups
116
7
Problems 5
123
2
Hermitian and Inner Product Spaces
125
34
Hermitian and Inner Products, and Norms
126
13
Unitary and Self-adjoint Maps
139
10
Orthogonal and Symmetric Maps
149
4
Problems 6
153
6
Selected Topics
159
36
The Geometry of Real Quadratic Forms
159
10
Normed Algebras, Quaternions and Cayley Numbers
169
9
Introduction to the Representation of Finite Groups
178
12
Problems 7
190
5
Appendix A --- Set Theory
195
10
Sets and Maps
195
7
Problems A
202
3
Appendix B --- Answers and Solutions to the Problems
205
34
Bibliography
239
2
Index
Notation Index
241
2
Definition Index
243
1
Theorem Index
244
1
Subject Index
245