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| Àâòîðèçàöèÿ |
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| Ïîèñê ïî óêàçàòåëÿì |
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| Finkbeiner D.T. — Introduction to Matrices and Linear Transformations |
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| Ïðåäìåòíûé óêàçàòåëü |
Matrix, characteristic values of 126—133 136—141 146 155 185— 191 198—202 206-207
Matrix, characteristic vectors of 126—133 135—141 185—186 191 201-202
Matrix, conjugate of 184—185 189
Matrix, continuity of 202
Matrix, derivative of 202—204
Matrix, determinant of 88—96
Matrix, diagonability of 130— 133 136—141 189
Matrix, diagonal 69 72 129—132 136—142 166—167 186 189 200
Matrix, elementary divisors of 157—158
Matrix, hermitian 190—191
Matrix, idempotent 70 72 75 125 139
Matrix, identity 68
Matrix, impedance 124
Matrix, integral of 202
Matrix, inverse of 70 72 97—99 103—104 113—114 118—120 159—161 180 200 227
Matrix, Jordan form of 153—158 196—198 206
Matrix, largest characteristic value of 200—201
Matrix, Lorentz 79—80
Matrix, main diagonal of 69
Matrix, Markov 79 130
Matrix, minimal polynomial of 134—137 157—158 185
Matrix, nilpotent 70 76 142—155 196—197 207
Matrix, non-singular 70 72 78
Matrix, orthogonal 180 186
Matrix, Pauli 79
Matrix, permutation 109 224—227
Matrix, pivot operations on 102—105 222—228
Matrix, rank of 76— 79 85 118
Matrix, row operations on 108—110
Matrix, scalar 68—69 72 199
Matrix, scalar multiple of 65
Matrix, Segre characteristic of 157—158
Matrix, singular 70 99
Matrix, skew-symmetric 71—72 99 166 168 182—183
Matrix, strictly triangular 70 72
Matrix, symmetric 71—72 120 166—167 183— 191
Matrix, trace of 159—161 191 198 204
Matrix, transpose of 71 85
Matrix, triangular 69 72 78 128 197
Matrix, unitary 181 191
Matrix, Vandermonde 96 100 199
Matrix, zero 65
Member of a set 4
Metric 184
Metric space 173
Minimal polynomial 134—137 157—158 185
Monic polynomial 134
Nilpotent linear transformations 48 54 76 133 142—155
Nilpotent matrices 70 76 133 142—155 195—197 207
Non-homogeneous system 86
Non-singular linear transformation 55—57 153
Non-singular matrix 70 72 78
Normal orthogonal basis 176—180 186 189
Normal vector 176
Null space of a linear transformation 52—54 142 153
Nullity of a linear transformation 52—54
Operation,  -ary 211
Operation, binary 14 211
Operation, closed 13 17— 19 211
Operation, elementary 101 108 117
Operation, pivot 102 222—228
Operation, unary 14
Ordered -tuple 209
Ordered pair 8
Orthogonal, complement of a subspace 175 178
Orthogonal, Matrix 180 186
Orthogonal, projection 143 145 174—175 178 200
Orthogonal, transformation 178—182 185—186
Orthogonality of vectors 172—178 185
Orthogonality, Gram — Schmidt process for 174—175 178
Orthonormal 176
Parallelogram principle 24
Parseval’s identity 178
Partition 213—214 217 220
Pauli matrices 79
Permutation 92
Permutation matrix 109 224—227
Perpendicularity, see Orthogonality Pivot operations 102 222—228
Polynomial, characteristic 128 133 136 157—159 185
Polynomial, minimal 134—137 157—158 185
Polynomial, monic 134
Polynomial, space of 26 28 37 49 57
Positive definite 170 183 188—189
Postulates 14
Postulates, for a Boolean algebra 15
Postulates, for a field 19
Postulates, for a group 18
Postulates, for a linear algebra 49
Postulates, for a vector space 26
Principal Axes Theorem 185—186
Product, dot 165 169 176
Product, inner 169—182
Product, of cosets 216
Product, of linear transformations 45—46
Product, of mappings 13
Product, of matrices 66 78
Projection 47 143—146 161 174—175 178 200
Projection, orthogonal 143 145 174—175 178 200
Projection, supplementary 143 145 200
Proper states 127
Proper values 127
Proper vectors 127
Pythagorean Theorem 177
Quadratic form 182—191
Quadratic form, positive definite 183 188—189
Quadratic form, rank of 187—188
Quadratic form, real symmetric 183
Quadratic form, signature of 187—188
Quadratic function 182—191
Quadric surface 184
Quaternions 51 68
Quotient system 217
Range, of a function 10 210
Range, of a relation 210
Range, space of a linear transformation 52— 54 114 142 153
Rank, of a bilinear form 164
Rank, of a bilinear function 164
Rank, of a linear transformation 52—54
Rank, of a matrix 76—79 85 118
Rank, of a quadratic form 187—188
Reflexive relation 107 213
Relation, binary 209—210
Relation, cosets of a 214 220
Relation, domain of a 210
Relation, equivalence 13 104 106—125 164—168 190—191 213—215 220 222-228
Relation, induced 214—215
Relation, range of a 210
Relation, reflexive 107 213
Relation, symmetric 107 213
Relation, transitive 107 213
| Right hand notation 45 77 85
Rigid motion 178—182 185—186
Rotations 21 47 181
Row, equivalence of matrices 110—116
Row, index 64
Row, operations on matrices 108—110
Row, vector 71 77—78 177 180 182
scalar 26
Scalar, matrix 68—69 72 199
Scalar, multiple of a linear transformation 45—46
Scalar, multiple of a matrix 65
Scalar, multiple of a vector 24—26
Scalar, polynomial 134
Scalar, product, see Dot product Schwarz inequality 171—173
Segre characteristic 157—158
Sequences of matrices 193—199
Sequences of numbers 193
Series, of matrices 193—199
Series, of numbers 193
Series, power 193—195
Series, Taylor 190 193
Set 3—10 13—15 17 209-212
Set, proper subset of a 5
Set, subset of a 5
Set, void 4—5
Sets, cartesian product of 8 209
Sets, complementation of 6 15
Sets, difference of 9
Sets, disjoint 6
Sets, equality of 5
Sets, intersection of 6 15 17
Sets, operations on 6 15
Sets, symmetric difference of 9
Sets, union of 6 15 17
Signature of a quadratic function 187—188
Similarity of matrices 120—126 130 136—141 151 156 180 186-187
Similarity, canonical form for 156
Singular linear transformation 55
Singular matrix 70 99
Skew — Hermitian matrix 191
Skew-symmetric matrix 71—72 99 166 168 182—183
Space, see Vector space Stochastic matrix, see Markov matrix Subset 5
Subset, proper 5
Subset, relation 5 15
Subsets, system of 13 15
subspace 29—32
Subspace,  -invariant 54 144—155
Subspace, annihilator of 76
Subspace, cyclic 145
Subspace, mapping of 48
Subspace, null 52—54 142 153
Subspace, orthogonal complement of 175 178
Subspace, range 52—54 114 142 153
Subspace, spanned by characteristic vectors 129 139 145 153
Subspace, spanned by vectors 30
Subspaces, dimensions of 39—40
Subspaces, intersection of 30—32
Subspaces, sum of 30—32
Sum, direct 143—155
Sum, of linear transformaions 45—46
Sum, of matrices 65
Sum, of subspaces 30—32
Sum, of vectors 24—26
Superdiagonal 142
Supplementary projection 143 145 200
Symmetric, difference of sets 9—10
Symmetric, matrix 71—72 120 166—167 183 185-191
Symmetric, relation 107 213
Symmetry, conjugate 170
Symmetry, Hermitian 170
Symmetry, of inner product 170
System of linear equations, augmented matrix of 86
System of linear equations, consistent 87
System of linear equations, equivalence of 101 116 227
System of linear equations, homogeneous 86
System of linear equations, matrix of 84
System of linear equations, non-homogeneous 86
System of linear equations, operations on 100—105
System of linear equations, solution by Cramer’s rule 98—99
System of linear equations, solution by pivot operations 102 222—227
System of linear equations, solution of 84
System, see Abstract systems System of linear equations 84—89 98—105 222-228
Taylor expansion 190 193
Trace of a linear transformation 160—161
Trace of a matrix 159—161 191 198 204
Transitive relation 107 213
Transpose of a matrix 71 85
Transposition 91
Triangle inequality 173
Triangular matrix 69 72 78 128 197
Triangular matrix, strictly 70 72
Tucker, A. W. 222
Union of sets 6 15 17
Unitary, matrix 181 191
Unitary, space 170—171 181 191
Unitary, transformation 179 181
Vandermonde matrix 96 100 199
Vector space 23—43 (see also Subspace)
Vector space, dimension of 38—40
Vector space, dual 75—76 162
Vector space, Euclidean 170 173 175—179
Vector space, inner product 181
Vector space, of -tuples 27 35—36 42
Vector space, of continuous functions 28 170—171
Vector space, of polynomials 26 28 37 49 57
Vector space, of real numbers 27
Vector space, of solutions of a differential equation 28 205 207
Vector space, subspace of 29—32
Vector space, unitary 170—171 181 191
Vector spaces, direct sum of 143—155
Vector, addition 24—26
Vector, characteristic 126—133 135—141 185—186 189 191 201-202
Vector, column 71 77 89 177
Vector, components 23
Vector, length of 162 169 172—179
Vector, multiplication by scalars 24—26
Vector, normal 176
Vector, representation by a matrix 77
Vector, row 71 77—78 177 180 182
Vectors, dot product of 165 169 176
Vectors, inner product of 169—182
Vectors, orthogonal 172—178 185
Vectors, orthonormal 176
Vectors, sum of 24—26
Venn diagrams 5—6
Void set 4—5
Zero, mapping 13
Zero, matrix 65
Zero, subspace 29
Zero, transformation 46
Zero, vector 27
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