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Hoffman K., Kunze R. — Linear algebra
Hoffman K., Kunze R. — Linear algebra

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Название: Linear algebra

Авторы: Hoffman K., Kunze R.

Аннотация:

This introduction to linear algebra features intuitive introductions and examples to motivate important ideas and to illustrate the use of results of theorems.


Язык: en

Рубрика: Математика/Алгебра/Линейная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 1971

Количество страниц: 407

Добавлена в каталог: 19.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$F^n$      29
$F^{m\times n}$      29
Adjoint of transformation      295
Adjoint, classical      148 159
Admissible subspace      232
Algebra      117
Algebra of formal power series      119
Algebra, self-adjoint      345
Algebraically closed field      138
Alternating n-linear function      144 169
Annihilator of subset      101
Annihilator of sum and intersection      106(Ex. 11)
Annihilator of vector (T-annihilator)      201 202 228
Approximation      283
Associativity      1
Associativity of matrix multiplication      19 90
Associativity of vector addition      28
Augmented matrix      14
Axiom of Choice      400
Basis      41
Basis, change of      92
Basis, dual      99 165
Basis, for module      164
Basis, ordered      50
Basis, orthonormal      281
Basis, standard basis of $F^n$      41
Bessel's inequality      287
Bilinear form      166 320 359
Bilinear form, diagonalization of      370
Bilinear form, group preserving      379
Bilinear form, matrix of      362
Bilinear form, non-degenerate (non-singular)      365
Bilinear form, positive definite      368
Bilinear form, rank of      365
Bilinear form, signature of      372
Bilinear form, skew-symmetric      375
Bilinear form, symmetric      367
Cauchy — Schwarz inequality      278
Cayley transform      309 (Ex. 7)
Cayley — Hamilton theorem      194 237
Characteristic of a field      3
Characteristic polynomial      183
Characteristic space      182
Characteristic value      182 183
Characteristic vector      182
Classical adjoint      148 159
Coefficients of polynomial      120
Cof actor      158
Column equivalence      256
Column operations      26 256
Column rank      72 114
Commutative algebra      117
Commutative group      83
Commutative ring      140
Companion matrix      230
Complementary subspace      231
Complementary subspace, orthogonal      286
composition      390
Conductor      201 202 232
Congruence      139 393 396
conjugate      271
Conjugate, transpose      272
Conjugation      276 (Ex. 13)
Coordinate matrix      51
coordinates      50
Coset      177 396
Cramer's rule      161
Cyclic decomposition theorem      233
Cyclic subspace      227
Cyclic vector      227
Degree of multilinear form      166
Degree of polynomial      119
Dependence, linear      40 47
Derivative of polynomial      129 266
Determinant function      144
Determinant function, existence of      147
Determinant function, for linear transformations      172
Determinant function, uniqueness of      152
Determinant rank      163 (Ex. 9)
Diagonalizable operator      185
Diagonalizable part of linear operator      222
Diagonalizable, simultaneously      207
Diagonalizatio, unitary      317
Diagonalization      204 207 216
Diagonalization of Hermitian form      323
Diagonalization of normal matrix (operator)      317
Diagonalization of self-adjoint matrix (operator)      314
Diagonalization of symmetric bilinear form      370
Differential equations      223 (Ex. 14) 249
DIMENSION      44
Dimension, formula      46
Direct sum      210
Direct sum of matrices      214
Direct sum of operators      214
Direct sum, invariant      214
Disjoint subspaces      See Independent subspaces
Distance      289 (Ex. 4)
Division with remainder      128
Dual basis      99 165
Dual module      165
Dual space      98
Eigenvalue      See Characteristic value
Elementary column operation      26 256
Elementary Jordan matrix      245
Elementary matrix      20 253
Elementary row operation      6 252
Empty set      388
Entries of a matrix      6
Equivalence relation      393
Equivalent systems of equations      4
Euclidean space      277
Exterior (wedge) product      175 177
Factorization of polynomial      136
Factors, invariant      239 261
Field      2
Field, algebraically closed      138
Field, subfield      2
Finite-dimensional      41
Finitely generated module      165
Form, alternating      169
Form, bilinear      166 320 359
Form, Hermitian      323
Form, matrix of      322
Form, multilinear      166
Form, non-degenerate,      324 (Ex. 6)
Form, non-negative      325
Form, normal      257 261
Form, positive      325 328
Form, quadratic      273 368
Form, r-linear      166
Form, rational      238
Form, sesqai-linear      320
Formal power series      119
Free module      164
Function      389
Function, determinant      144
Function, identity      390
Function, inverse of      391
Function, invertible      390
Function, linear      67 97 291
Function, multilinear      166
Function, n-linear      142
Function, polynomial function      30
Function, range of      389
Function, restriction of      391
Fundamental theorem of algebra      138
Gram — Schmidt process      280 287
Grassman ring      180
Greatest common divisor      133
Group      82
Group, commutative      83
Group, general linear      307
Group, Lorentz      382
Group, orthogonal      380
Group, preserving a form      379
Group, pseudo-orthogonal      381
Group, symmetric      153
Hermitian      See Self-adjoint
Hermitian form      323
Homogeneous system of linear equations      4
Hyperspace      101 109
Ideal      131
Ideal, principal ideal      131
Idempotent transformation      See Projection
Identity element      117 140
Identity function      390
Identity matrix      9
Identity, resolution of      337 344
Independence, linear      40 47
Independent linearly      40 47
Independent subspaces      209
Inner product      271
Inner product, matrix of      274
Inner product, quadratic form of      273
Inner product, space      277
Inner product, standard      271 272
Integers      2
Integers, positive      2
Interpolation      124
Intersection      388
Intersection of subspaces      36
Invariant direct sum      214
Invariant factors of a matrix      239 261
Invariant subset      392
Invariant subspace      199 206 314
inverse of function      391
Inverse of matrix      22 160
Inverse, left      22
Inverse, right      22
Inverse, two-sided      22
Invertible function      390
Invertible linear transformation      79
Invertible matrix      22 160
Irreducible polynomial      135
Isomorphism of inner product spaces      299
Isomorphism of vector spaces      84
Jordan form of matrix      247
Kronecker delta      9
Lagrange interpolation formula      124
Laplace expansions      179
Left inverse      22
Linear algebra      117
Linear combination of equations      4
Linear combination of vectors      31
Linear equations      See System of linear equations
Linear functional      97
Linear transformation (operator)      67 76
Linear transformation (operator), adjoint of      295
Linear transformation (operator), cyclic decomposition of      233
Linear transformation (operator), determinant of      172
Linear transformation (operator), diagonalizable      185
Linear transformation (operator), diagonalizable part of      222
Linear transformation (operator), invertible      79
Linear transformation (operator), matrix in orthonormal basis      293
Linear transformation (operator), matrix of      87 88
Linear transformation (operator), minimal polynomial of      191
Linear transformation (operator), nilpotent      222
Linear transformation (operator), non-negative      329 341
Linear transformation (operator), non-singular      79
Linear transformation (operator), normal      312
Linear transformation (operator), nullity of      71
Linear transformation (operator), orthogonal      303
Linear transformation (operator), polar decomposition of      343
Linear transformation (operator), positive      329
Linear transformation (operator), product of      76
Linear transformation (operator), quotient      397
Linear transformation (operator), range of      71
Linear transformation (operator), rank of      71
Linear transformation (operator), self-adjoint      298 314
Linear transformation (operator), semi-simple      263
Linear transformation (operator), trace of      106 (Ex. 15)
Linear transformation (operator), transpose of      112
Linear transformation (operator), triangulable      202
Linear transformation (operator), unitary      302
Linearly dependent (independent)      40 47
Lorentz group      382
Lorentz transformation      311 (Ex. 15) 382
Matrix      6
Matrix, augmented      14
Matrix, classical adjoint of      148 159
Matrix, coefficient      6
Matrix, cofactors      158
Matrix, companion      230
Matrix, conjugate transpose      272
Matrix, coordinate      51
Matrix, elementary      20 253
Matrix, elementary, Jordan      245
Matrix, identity      9
Matrix, invariant factors of      239 261
Matrix, inverse of      22 160
Matrix, invertible      22 160
Matrix, Jordan form of      247.
Matrix, minimal polynomial of      191
Matrix, nilpotent      244
Matrix, normal      315
Matrix, of bilinear form      362
Matrix, of form      322
Matrix, of inner product      274
Matrix, of linear transformation      87 88
Matrix, orthogonal      162(Ex. 4) 380
Matrix, positive      329
Matrix, principal minors of      326
Matrix, product      17 90
Matrix, rank of      114
Matrix, rational form of      238
Matrix, row rank of      56 72 114
Matrix, row-reduced      9
Matrix, row-reduced echelon      11 56
Matrix, self-adjoint (Hermitian)      35 314
Matrix, similarity of      94
Matrix, skew-symmetric      162 (Ex. 3) 210
Matrix, symmetric      35 210
Matrix, trace of      98
Matrix, transpose of      114
Matrix, triangular      155 (Ex. 7)
Matrix, unitary      163 (Ex. 5) 303
Matrix, upper-triangular      27
Matrix, Vandermonde      125
Matrix, zero      12
Minimal polynomial      191
Module      164
Module, basis for      164
Module, dual      165
Module, finitely generated      165
Module, free      164
Module, rank of      165
Monic polynomial      120
Multilinear function (form)      166
Multilinear function (form), degree of      166
Multiplicity      130
n-linear function      142
n-linear function, alternating      144 169
n-tuple      29
Nilpotent matrix      244
Nilpotent operator      222
Non-degenerate bilinear form      365
Non-degenerate form      324 (Ex. 6)
Non-negative form      325
Non-negative operator      329 341
Non-singular form      See Non-degenerate
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