Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Horn R.A. — Matrix Analysis
Horn R.A. — Matrix Analysis

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Matrix Analysis

Автор: Horn R.A.

Аннотация:

Matrix Analysis presents the classical and recent results for matrix analysis that have proved to be important to applied mathematics.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1990

Количество страниц: 529

Добавлена в каталог: 16.10.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
a priori bounds      337
Absolute convergence      279 300
Absolute value of a complex number      532
Absolute vector norm      285 310 365 438
Additive property, of inner product      260
Adjacency matrix, of a graph      168 523
Adjoint, classical      20
Adjoint, Hermitian      6
Adjugate      20
Algebraic multiplicity      58 60 138 141 497 499
Algebraically closed field      41 537
Algebraically simple eigenvalue      371 500 508
Alternating sum      8
Angle between vectors      15
Annihilate      142
Antilinear transformation      250
Approximation problems      332 427
ARC      357
arg      532
Argument of a complex number      532
Arithmetic-geometric mean inequality      535
Augmented matrix      11 12
Back substitution      159
Backward identity      28 207
Ball of radius r      281 541
Basis      3
Basis, change of      30
Basis, orthonormal      16
Basis, representation      31
Bilinear form      169 175
Biorthogonality      59
Birkhoff’s theorem      197 527
Block, diagonal matrices      24
Block, triangular matrices      25
Bochner’s theorem      394
Bordered matrix      185
Bound norm      294
Boundary      282
Bounded set      282 541
Brauer, condition for invertibility      381
Brauer, region      380
Brauer, theorem      380
Brualdi, condition for invertibility      389
Brualdi, region      385
Brualdi, theorem      385 387
Cancellation theorem      78 141
Canonical forms, consimilarity      251
Canonical forms, integer matrices      158
Canonical forms, irreducible normal form      506
Canonical forms, Jordan      121
Canonical forms, polar      156 412ff
Canonical forms, rational      154
Canonical forms, rational canonical      156
Canonical forms, rational matrices      158
Canonical forms, real Jordan      152
Canonical forms, real orthogonal matrices      108
Canonical forms, real skew-symmetric matrices      107
Canonical forms, real symmetric matrices      107
Canonical forms, singular value decomposition      157 414ff
Canonical forms, symmetric Jordan      209
Canonical forms, triangular factorization      157
Carmichael and Mason’s bound on zeroes      317 318 364
Cassini, ovals of      380
Cauchy bound on zeroes      316 318 364
Cauchy sequence      274
Cauchy — Binet formula      22
Cauchy — Schwarz inequality      15 261 277 535 536
Cayley — Hamilton theorem      86
Cesaro summation      524
Change of basis matrix      32 33
Characteristic equation      87
Characteristic polynomial      38 86 87 540
Characteristic polynomial, Cayley — Hamilton theorem      86
Characteristic polynomial, definition      38
Characteristic polynomial, positive definite matrix      403
Cholesky factorization      114 407
Circulant matrices      26
Classical adjoint      20
Closed set      282 541
Closure      282
Cofactor      17
Column rank      12
Combinatorially symmetric matrix      523
Commutative ring      95
Commutator      98
Commuting family      51 81 99 139
Commuting matrices      135
Compact set      282 541
Companion matrix      147 149 316 514
Compatible vector norm      294 324 327
Completeness property of a vector space      274
Complex conjugate      531
complex numbers      531 532
Compound matrix      19
Concave function      534
Concave logarithm of determinant      466
Concave trace of inverse      468
Condiagonalization      244 248
Condition number      336 340 365 366 374 442
Coneigenvalue characterization      246
Coneigenvalue definition      245
Coneigenvector      245
conformal      17
Congruence, $^{T}congruence$      220
Congruence, *congruence      220 399 464ff 470
Congruence, simultaneous *congruence, canonical pairs      236
Conjugate linear      169
Conjunctive      220
Consimilarity      234 244
Consimilarity, characterizations      251
Consimilarity, to a real matrix      255
Consistent linear equations      12
Consistent vector norm      324
Constrained extrema      34
Continuous dependence of eigenvalues      540
Continuous dependence of zeroes      539
Continuous function, maximum of a      541
Contriangularization      244
Convergence of a sequence      269
Convergent matrix      137 298
Convex      284
Convex, combination      535
Convex, cone      463
Convex, function      392 533 534—536
Convex, hull      533
Convex, metric hull      289
Convex, sets      533—536
Coordinate representation      30
Correlation matrix      400
Courant — Fischer theorem      179 420 424 472
Covariance matrix      219 239 392 424
Cramer’s Rule      21
CYCLE      357
Cyclic of index k      514
Defect from normality      316
Defective      58
Deflation      63 83
Deleted absolute row sums      344
Dependent      3
Determinant      7 11 398
Determinantal inequalities      453 467 476—486
Determinantal inequalities, Fischer      478
Determinantal inequalities, Gersgorin      351
Determinantal inequalities, Hadamard      477
Determinantal inequalities, Hadamard — Fischer      485
Determinantal inequalities, Minkowski      482
Determinantal inequalities, Oppenheim      480
Determinantal inequalities, Ostrowski — Taussky      481
Determinantal inequalities, Szasz      479
Diagonal entries, equal      77
Diagonal matrix      23
Diagonalizable      139 145
Diagonalizable, almost      89
Diagonalizable, by orthogonal similarity      211
Diagonalizable, definition      46
Diagonalizable, orthogonally      101
Diagonalizable, simultaneously      49
Diagonalizable, unitary      101
Diagonalization by congruence      228
Diagonalization by consimilarity      234 244 248
Diagonalization by similarity      46 145
Diagonalization by unitary congruence      204
Diagonalization by unitary consimilarity      244 245
Diagonalization by unitary similarity      101
Diagonalization, simultaneous      52
Diagonally dominant      349
Diagonally dominant, strictly      302 349
Difference scheme      394
Differential equations      132 394
Differential equations, elliptic      239 459
Differential equations, hyperbolic      239
Differential equations, partial      168 216 218
DIMENSION      4
Direct sum      24
Directed graph of a matrix      357 517 522
Directed path      357
Dominant eigenvalue      506
Doubly stochastic matrix      197 527—529
Dual norm      275 410
Dual norm of Euclidean norm      277
Dual pair      278
Duality theorem      287
Edges      168
Eigenspace      57
Eigenvalue, algebraic multiplicity      58 60 138 141 497 499
Eigenvalue, algebraically simple      371
Eigenvalue, continuous dependence on matrix entries      540
Eigenvalue, definition      35
Eigenvalue, deflation to calculate      63
Eigenvalue, distinct      48
Eigenvalue, dominant      506
Eigenvalue, generalized      213
Eigenvalue, geometric multiplicity      58 60 138 141 497 498
Eigenvalue, ill-conditioned      367
Eigenvalue, inclusion region      501
Eigenvalue, inclusion theorem      177
Eigenvalue, index of      131 139 148
Eigenvalue, location      343
Eigenvalue, moments      43
Eigenvalue, nonnegative matrix      489
Eigenvalue, of a sum      181 184
Eigenvalue, perfectly conditioned      367
Eigenvalue, perturbation      198 343 364
Eigenvalue, positive definite matrix      402
Eigenvalue, positive matrix      496
Eigenvalue, power method to calculate      62
Eigenvalue, principal submatrices      189
Eigenvalue, variational characterization      176—180
Eigenvalue, well-conditioned      367
Eigenvector      57
Eigenvector, definition      35
Eigenvector, left      59 371
Eigenvector, positive      493 494 495 513
Eigenvector, right      59
Elementary divisors      155
Elementary symmetric functions      41
Elliptic differential operator      239
Equilibrated      283
Equivalence relation, congruence      221
Equivalence relation, consimilarity      251
Equivalence relation, definition      45
Equivalence relation, vector seminorm      262
Equivalent matrices      164
Equivalent vector norms      273 279
Equivalent, orthogonally      73
Equivalent, real orthogonally      73
Equivalent, unitarily      72
Error analysis      335
Essentially nonnegative matrix      506
Essentially triangular matrix      26
Euler’s theorem      111
Exponential of a matrix      300
Extreme points, closed convex set      533
Extreme points, doubly stochastic matrices      528
Extreme ray, definition      463
Extreme ray, positive semidefinite matrices      464
Factor analysis      431
Factorizations      156
Factorizations, Cholesky      114 407
Factorizations, complex skew-symmetric matrix      217
Factorizations, complex symmetric matrix      204
Factorizations, LU      158—165
Factorizations, polar      156 411 412ff
Factorizations, product of two Hermitian matrices      172
Factorizations, QR      112 164 406
Factorizations, singular value decomposition      411
Factorizations, Takagi      250 423 466
Factorizations, triangular      157
Family, commuting      51 81 99 139
Family, commuting real normal      108 112
Family, complex symmetric      243
Family, diagonalizable symmetric      217
Family, Hermitian      172
Family, normal      103
Family, simultaneous condiagonalization      252
Family, simultaneous diagonalization by *congruence      239
Family, simultaneous diagonalization by unitary $^{T}congruence$      243
Family, simultaneous singular value decomposition      426
Family, simultaneous triangularization      84
Fan, k norms      445
Fan, theorem on eigenvalue location      501
Fejer, trace theorem, on positive semidefinite matrices      459
Fejer, uniqueness theorem, for elliptic partial differential equations      460
Field      1
Field of values      321 332
Fischer’s inequality      478
Forms, bilinear      169 175
Forms, hermitian      174
Forms, quadratic      168 174 214 466
Forms, sesquilinear      169
Forward substitution      159
Fundamental theorem of algebra      537
General linear group      14
Generalized coordinates      227
Generalized eigenvalue      213
Generalized inverse      421
Generalized matrix functions      8
Generalized matrix norm      290 320 see
Geometric multiplicity      58 60 138 141 497 498
Gersgorin circles      346
Gersgorin disc theorem      344
Gersgorin discs      345 353
Gersgorin region      345
Givens’s method      77
Gram matrix      407
Gram — Schmidt process      15 148
Gram — Schmidt process, modified      116
Gram — Schmidt process, symmetric analogue      211
Graph      168
Greub and Rheinboldt inequality      452
Group, finite abelian      510
Group, general linear      14
Group, isometry      266 267
Group, orthogonal      69 71
Group, unitary      69
Grunsky inequalities      202
Hadamard — Fischer inequalities      485
Hadamard, exponential of a matrix      461
Hadamard, inequality      199 200 477 483
Hadamard, powers of a matrix      462
1 2 3 4
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте