Электронная библиотека Попечительского советамеханико-математического факультета Московского государственного университета
 Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум Авторизация Поиск по указателям     Hoffman K., Kunze R. — Linear algebra Обсудите книгу на научном форуме Нашли опечатку?Выделите ее мышкой и нажмите Ctrl+Enter 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: 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 Предметный указатель 29 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 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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