A (Terse) Introduction to Linear Algebra (Student Mathematical Library, Vol. 44)

Title......Page 1
Contents......Page 3
Preface......Page 7
1.1 Groups and fields......Page 9
1.2 Vector spaces......Page 12
1.3 Linear dependence, bases, and dimension......Page 22
1.4 Systems of linear equations......Page 30
*1.5 Normed finite-dimensional linear spaces......Page 40
2.1 Linear operators......Page 43
2.2 Operator multiplication......Page 47
2.3 Matrix multiplication......Page 49
2.4 Matrices and operators......Page 54
2.5 Kernel, range, nullity, and rank......Page 59
*2.6 Operator norms......Page 64
3.1 Linear functionals......Page 65
3.2 The adjoint......Page 70
4.1 Permutations......Page 73
4.2 Multilinear maps......Page 77
4.3 Alternating n-forms......Page 82
4.4 Determinant of an operator......Page 84
4.5 Determinant of a matrix......Page 87
5.1 The characteristic polynomial......Page 93
5.2 Invariant subspaces......Page 96
5.3 The minimal polynomial......Page 101
6.1 Inner products......Page 111
6.......Page 10
6.3 Self-adjoint operators......Page 121
6.4 Normal operators......Page 127
6.5 Unitary and orthogonal operators......Page 129
*6.6 Positive definite operators......Page 135
*6.7 Polar decomposition......Page 136
*6.8 Contractions and unitary dilations......Page 140
7.1 Reducing subspaces......Page 143
7.2 Semisimple systems......Page 150
7.3 Nilpotent operators......Page 155
7.4 The Jordan canonical form......Page 159
*7.5 The cyclic decomposition, general case......Page 160
*7.6 The Jordan canonical form, general case......Page 164
8.1 Functions of an operator......Page 167
8.2 Quadratic forms......Page 170
8.3 Perron-Frobenius theory......Page 174
8.4 Stochastic matrices......Page 186
8.5 Representation of finite groups......Page 188
A.l Equivalence relations-partitions......Page 195
A.2 Maps......Page 196
A.3 Groups......Page 197
A.4 Group actions......Page 202
A.5 Rings and algebras......Page 204
A.6 Polynomials......Page 209
Index......Page 219
Symbols......Page 223
Titles in This Series......Page 225