151
62
146
33
65
17
10
43
35
140
28
2
4
123
5
5
4
5
2
2
88
5
26
43
20
24
34
131
41 151
23
2
47
27
88
18
90
28
40 95
43
90
17
176
176
118 121
(p,q) 44
(x,y) 119 121
A' 79
A* 132
Adjoint 79 86
Algebraically closed 104
Alternating form 50
Alternating group 47
Annihilator 26
Automorphism 86
Basis 10
Bessel's inequality 124
Bilinear form 36
Bilinear functional 21 36
Bounded from below 177
Bounded transformation 176
Cartesian decomposition 136
Cayley transform 145
Characteristic equation, polynomial, root 101
Characteristic of a field 2
Classical canonical form 114
Cogredient 83
column 65
Column rank 91
Complement 18
Complete metric space 176 189
Complete orthonormal set 122
Complex vector space 4
Complexification 41 151
Congruent transformations 134
Congruent vectors 35
Conjugate bilinear form 122
Conjugate isomorphism 131
Conjugate permutations 46
Conjugation 145
Contragredient 83
Contravariant 83
Convergence 175 183
Convex 162
Coordinate space 4 5
Coordinate system 10
Coset 33
Covariant 83
CYCLE 44
Degenerate 37
DET 99
Determinant 99
Diagonable 108
Diagonal form 108
DIM 19
DIMENSION 14
Direct sum 28
Disjoint cycles 44
Disjoint subspaces 17
Dual basis 23
Dual space 21
Elementary divisor 114
Equivalence relation 35
Equivalent 87
Ergodic theorem 185
Euclidean space 121
Even permutation 47
Even polynomial 19
exp A 186
External direct sum 30
Extreme point 162
Field 2
Finite-dimensional vector space 10
Gram — Schmidt orthogonalization process 128
Gramian 142
Graph 134
Group 44
Hadamard product 174
Hamilton — Cayley equation 115
Hermitian symmetry 122
Hermitian transformation 135
Hilbert space 189
Hochschild, G.P. 198
Homogeneous functional 20
Homogeneous transformation 55
Idempotent 73
Identity 43
Im 126
Image 88
Imaginary part of a complex number 126
Imaginary part of a transformation 137
Independent 32
INDEX 109
inf 176
Infimum 176
Inner product 119 121
| Inner product space 121
Internal direct sum 30
Intersection 17
Invariant 71
Inverse of a permutation 43
Inverse of a transformation 62
Invertible 62
Involution 78
Isometric matrix 144
Isometry 143
Isomorphism 14
Jordan form 114
Kronecker product 98
Lattice 142
Law of nullity 92
Left inverse 64
Length 121
linear combination 9
Linear dependence 7
Linear functional 20
Linear independence 7
Linear manifold 16
Linear transformation 55 57
Lower bound 180
Matrix 65
Minimal polynomial 114
Minimax principle 181
Module 5
Multilinear form 48
Multiplicity 103
Multiplicity of elementary divisors 114
Multiplicity, algebraic 104
Multiplicity, geometric 104
Neumann series 186
Nilpotent 109
Non-degenerate 37
Non-singular 99
Norm 121
Norm of a linear transformation 176
normal 159
Normed vector space 126
NULL-SPACE 88
Nullity 90
Numerical range 162
Odd permutation 47
Odd polynomial 19
Operator 55
Order of a permutation 46
Origin 3
Orthogonal complement 123
Orthogonal dimension 122
Orthogonal equivalence 158
Orthogonal projections 147
Orthogonal transformation 142
Orthogonal vectors 122
Orthonormal 122
Orthonormal basis 128
Parity 47
Parseval's identity 124
Partial isometry 150
Permutation 42
Perpendicular projection 146
Polar decomposition 170
Polarization 138
Positive definite form 122
Positive matrix 141
Positive number 2
Positive transformation 140
Principal minor 167
Product of linear transformations 58
Product of permutations 42
Projection 73
Proper value 102
Proper vector 102
Quadratic form 38
Quotient space 34
r(A) 182
RANGE 88
Rank 90
Rational vector space 4
Re 126
Real part of a complex number 126
Real part of a transformation 137
Real transformation 137
Real vector space 4
Reducibility 72
Reflexivity 25 28
Riesz — Fischer theorem 189
Right inverse 64
Row 65
Row rank 91
scalar 1
Scalar product 119
Schwarz's inequality 125
Self-adjoint 135
sgn 47
Signum 47
Similar 85
Simple elementary divisor 114
Simple proper value 103
singular 99
Skew hermitian 136
Skew-symmetric form 50
Skew-symmetric transformation 136
span 17
Spectral form 156
Spectral radius 182
Spectral theorem 156
Spectrum 103
Strictly positive 140
Subgroup 47
subspace 16
Sup 176
Supremum 176
Sylvester's law of nullity 92
Symmetric bilinear form 38
Symmetric form 49
Symmetric group 44
Symmetric transformation 135
Tensor product of spaces 40
Tensor product of transformations 95
tr 105
Trace 105 109
TRANSPOSE 81
Transposition 44
Triangular form 107
Unitary equivalence 158
Unitary space 121
Unitary transformation 142
Upper bound 180
Vector 3
Vector space 3
Well-ordering 13
Zorn's lemma 13
[a] 65
[X,Y] 21
|