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| Hoffman K., Kunze R. — Linear algebra |
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| Предметный указатель |
Non-singular linear transformation 79
Norm 273
Normal form 257 261
Normal matrix 315
Normal operator 312
Null space 71
Nullity of linear transformation 71
Numbers, complex 2
Numbers, rational 3
Numbers, real 2
Onto 389
Operator, linear 76
Ordered basis 50
Orthogonal complement 285
Orthogonal equivalence of matrices 308
Orthogonal group 380
Orthogonal linear transformation 304
Orthogonal matrix 162 (Ex. 4) 380
Orthogonal projection 285
Orthogonal set 278
Orthogonal vectors 278 368
Orthogonalization 280
Orthonormal basis 281
Orthonormal set 278
Parallelogram law 276 (Ex. 9)
Permutation 151
Permutation, even, odd 152
Permutation, product of 153
Permutation, sign of 152
Polar decomposition 343
Polarization identities 274 368
Polynomial 119
Polynomial, characteristic 183
Polynomial, coefficients of 120
Polynomial, degree of 119
Polynomial, derivative of 129 266
Polynomial, function 30
Polynomial, irreducible (prime) 135
Polynomial, minimal 191
Polynomial, monic 120
Polynomial, primary decomposition of 137
Polynomial, prime (irreducible) 135
Polynomial, prime factorization of 136
Polynomial, reducible 135
Polynomial, root of 129
Polynomial, scalar 120
Polynomial, zero of 129
Positive definite 368
Positive form 325 328
Positive integers 2
Positive matrix 329
Positive operator 329
Power series 119
Primary components 351
Primary decomposition of polynomial 137
Primary decomposition theorem 220
Prime factorization of polynomial 136
Prime polynomial 135
Principal access theorem 323
Principal ideal 131
Principal minors 326
Product of linear transformations 76
Product of matrices 14 90
Product of permutations 153
Product, exterior (wedge) 175 177
Product, tensor 168
Projection 211
Proper subset 388
Pseudo-orthogonal group 381
Quadratic form 273 368
Quotient space 397
Quotient transformation 397
RANGE 71
Rank of bilinear form 365
Rank of linear transformation 71
Rank of matrix 114
Rank of module 165
Rank, column 72 114
Rank, determinant 163 (Ex. 9)
Rank, row 56 72 114
Rational form of matrix 238
Reducible polynomial 135
Relation 393
Relation, equivalence 393
Relatively prime 133
Resolution of the identity 337 344
Resolution, spectral 336 344
Restriction of function 391
Restriction operator 199
Right inverse 22
Rigid motion 310 (Ex. 14)
Ring 140
Ring, Grassman 180
Root of family of operators 343
Root of polynomial 129
Rotation 54 309
Row operations 6 252
| Row rank 56 72 114
Row space 39
Row vectors 38
Row-equivalence 7 58 253
Row-equivalence, summary of 55
Row-reduced matrix 9
Row-reduced matrix, row-reduced echelon matrix 11 56
scalar 2
Scalar, polynomial 120
Self-adjoint algebra 345
Self-adjoint matrix 35 314
Self-adjoint operator 298 314
Semi-simple operator 263
Separating vector 243(Ex. 14)
Sequence of vectors 47
Sesqui-linear form 320
Set 388
Set, element of (member of) 388
Set, empty 388
Shuffle 171
Sign of permutation 152
Signature 372
Similar matrices 94
Simultaneous diagonalization 207
Simultaneous triangulation 207
Skew-symmetric bilinear form 375
Skew-symmetric matrix 162 (Ex. 3) 210
Solution space 36
Spectral resolution 336 344
Spectral theorem 335
Spectrum 336
Square root 341
Standard basis of  41
Stuffer (das einstopfende Ideal) 201
Subfield 2
SubMatrix 163 (Ex. 9)
Subset 388
Subset, invariant 392
Subset, proper 388
subspace 34
Subspace, annihilator of 101
Subspace, complementary 231
Subspace, cyclic 227
Subspace, independent subspaces 209
Subspace, invariant 199 206 314
Subspace, orthogonal complement of 285
Subspace, quotient by 397
Subspace, spanned by 36
Subspace, sum of subspaces 37
Subspace, T-admissible 232
Subspace, zero 35
Sum of subspaces 37
Sum, direct 210
Symmetric bilinear form 367
Symmetric group 153
Symmetric matrix 35 210
System of linear equations 3
System of linear equations, homogeneous 4
T-admissible subspace 232
T-annihilator 201 202 228
T-conductor 201 202 232
Taylor's formula 129 266
Tensor 166
Tensor product 168
Trace of linear transformation 106(Ex.
Trace of matrix 98
Transformation, differentiation 67
Transformation, linear 67 76
Transformation, zero 67
Transpose of linear transformation 112
Transpose of matrix 114
Transpose, conjugate 272
Triangulable linear transformation 202 316
Triangular matrix 155 (Ex. 7)
Triangulation 203 207 334
union 388
Unitary diagonalization 317
Unitary equivalence of linear transformations 356
Unitary equivalence of matrices 308
Unitary matrix 163(Ex. 5) 303
Unitary operator 302
Unitary space 277
Unitary transformation 356
Upper-triangular matrix 27
Vandermonde matrix 125
Vector space 28
Vector space, basis of 41
Vector space, dimension of 44
Vector space, finite dimensional 41
Vector space, isomorphism of 84
Vector space, of n-tuples 29
Vector space, of polynomial functions 30
Vector space, of solutions to linear equations 36
Vector space, quotient of 397
Vector space, subspace of 34
Wedge (exterior) product 175 177
Zero matrix 12
Zero of polynomial 129
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