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Hogben L. — Handbook of Linear Algebra
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Íàçâàíèå: Handbook of Linear AlgebraÀâòîð: Hogben L. Àííîòàöèÿ: The Handbook of Linear Algebra provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use handbook format. The esteemed international contributors guide you from the very elementary aspects of the subject to the frontiers of current research. The book features an accessible layout of parts, chapters, and sections, with each section containing definition, fact, and example segments. The five main parts of the book encompass the fundamentals of linear algebra, combinatorial and numerical linear algebra, applications of linear algebra to various mathematical and nonmathematical disciplines, and software packages for linear algebra computations. Within each section, the facts (or theorems) are presented in a list format and include references for each fact to encourage further reading, while the examples illustrate both the definitions and the facts. Linearization often enables difficult problems to be estimated by more manageable linear ones, making the Handbook of Linear Algebra essential reading for professionals who deal with an assortment of mathematical problems.
ßçûê: Ðóáðèêà: Ìàòåìàòèêà /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Ãîä èçäàíèÿ: 2006Êîëè÷åñòâî ñòðàíèö: 1400Äîáàâëåíà â êàòàëîã: 30.06.2008Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
Ïðåäìåòíûé óêàçàòåëü
Jacobi rotation, singular value decomposition 45—11 to 45—12 Jacobi — Davidson methods 43—10 to 43—11 Jacobian characteristics, linearization 56—20 Jacobian characteristics, nonassociative algebra 69—2 Jacobi’s theorem 4—5 Jeffrey, David J. 72—1 to 72—21 Johnson association scheme 28—12 Johnson, Charles R. 34—1 to 34—15 Join, graphs 28—2 Join, Mathematica software, matrices manipulation 73—13 Join, Mathematica software, vectors 73—3 Jordan algebras, computational methods 69—21 Jordan algebras, nonassociative algebra 69—3 69—12 Jordan algebras, power associative algebras 69—15 Jordan Basis 6—3 6—4 6—5 Jordan blocks, Jordan canonical form 6—3 Jordan blocks, K-reducible matrices 26—9 Jordan blocks, linear differential equations 56—4 Jordan blocks, matrix function 11—4 Jordan blocks, matrix product 18—9 Jordan blocks, Perron — Schaefer condition 26—7 Jordan blocks, simultaneous similarity 24—10 Jordan canonical form see «real-Jordan canonical form» Jordan canonical form, canonical forms 6—3 to 6—6 Jordan canonical form, differential equations 55—6 55—8 Jordan canonical form, matrix function 11—1 to 11—2 11—4 Jordan canonical form, reducible matrices 9—8 Jordan canonical form, unitary similarity 7—3 Jordan characteristics, chain 6—4 Jordan characteristics, form matrices 56—3 Jordan characteristics, identity, nonassociative algebra 69—3 Jordan characteristics, invariants 6—3 6—4 Jordan characteristics, product, nonassociative algebra 69—3 Jordan characteristics, structures, simultaneous similarity 24—9 jordan command, Matlab software 71—9 Jordan — Wielandt matrix 17—2 JordanDecomposition, Mathematica software 73—18 JordanForm, Maple software 72—11 72—12 K-reducible matrices 26—8 to 26—13 k-step 44—3 Kahan matrix 17—4 Kahan — Cao — Xie — Li theorem 15—3 Kalman decomposition 57—7 to 57—8 Kalman filter 57—13 Kalman — Bucy filter, LTI systems 57—17 Kalman — Bucy filter, state estimation 57—11 57—12 57—13 Kamm and Nagy studies 48—9 Kantorovich Inequality 52—10 Kapranov rank 25—13 Karle — Hauptman matrix 60—7 to 60—9 Karp’s formula, max-plus eigenproblem 25—7 Karp’s formula, maximal cycle mean 25—5 Kaufman studies 44—4 Kernel, Bezout domains 23—8 Kernel, characters 68—5 Kernel, group representations 68—2 Kernel, least squares solution 39—4 Kernel, linear independence, span, and bases 2—6 Kernel, linear inequalities and projections 25—10 kernel, Mathematica software 73—1 Kernel, matrix representations 68—3 Kernel, range 3—5 to 3—6 Killing form, Malcev algebras 69—16 69—17 Killing form, semisimple and simple algebras 70—3 Kinetic energy, Lagrangian mechanics 59—5 Kinetic energy, oscillation modes 59—2 Kingman’s inequality 25—5 Kleene star 25—2 25—3 Kliemann, Wolfgang 6—14 56—1 Klienberg, Jon 63—9 Klyachko studies, eigenvalues 17—13 Klyachko studies, Hermitian matrices 8—4 Knott Inequality 52—10 Knutson and Tao studies, eigenvalues 17—13 Knutson and Tao studies, Hermitian matrices 8—4 Koteljanskii’s Determinantal Inequality 8—10 Kravcuk polynomials 28—12 Krein condition 28—11 Kreiss matrix theorem 16—10 kron function, Matlab software 71—4 Kronecker canonical form 55—7 to 55—10 Kronecker product, linear maps 13—9 Kronecker product, Matlab software 71—4 Kronecker product, matrix similarities 24—1 Kronecker product, partitioned matrices 10—8 to 10—9 Kronecker product, positive definite matrices 8—10 Kronecker product, rank and nullity 14—13 Kronecker product, semidefinite programming 51—3 51—4 Kronecker product, structured matrices 48—4 Kronecker product, tensor products 13—8 Kronecker symbol 28—11 Krylov characteristics, implicitly restarted Arnoldi method 44—11 to 44—12 Krylov characteristics, matrix, Lanczos method 42—19 Krylov characteristics, sequence 49—5 Krylov characteristics, spaces 41—2 Krylov characteristics, vectors 42—20 Krylov subspaces, eigenvalue computations 49—12 Krylov subspaces, iterative solution methods 41—2 to 41—4 Krylov subspaces, large-scale matrix computations 49—5 to 49—6 Krylov subspaces, projection 44—1 to 44—2 Krylov — Schur algorithm 43—9 Ky — Fan norms, polar decomposition 15—8 Ky — Fan norms, unitarily invariant norms 17—5 17—6 L-matrices, sign solvability 33—5 L-matrices, sign-pattern matrices 33—5 to 33—7 L-module 70—7 Lagrangian function 51—5 Lagrangian mechanics 59—5 to 59—6 Lagrangian properties, multiplier, differential equations 55—3 Lagrangian properties, primal-dual interior point algorithm 51—8 Lagrangian properties, relaxation 51—10 Laguerre polynomial 31—10 Lanczos algorithm, Krylov space methods 41—4 to 41—5 41—10 Lanczos algorithm, symmetric matrix eigenvalue techniques 42—19 to 42—21 Lanczos matrices, eigenvalue computations 49—12 Lanczos matrices, linear systems of equations 49—13 Lanczos matrices, symmetric Lanczos process 49—7 Lanczos methods, implicit restarting 44—6 Lanczos methods, pseudospectra computation 16—11 Lanczos methods, total least squares problem 48—9 Lanczos process 49—10 Lanczos vectors, Arnoldi factorization 44—3 Lanczos vectors, nonsymmetric Lanczos process 49—8 Lanczos vectors, symmetric Lanczos process 49—7 Landau’s theorem 27—9 Langou, Julien 74—1 to 74—7 75—1 77—1 Langville, Amy N. 63—1 to 63—14 LAPACK subroutine package, dense matrices 43—3 LAPACK subroutine package, DLAR2V subroutine 42—9 LAPACK subroutine package, DLARGV subroutine 42—9 LAPACK subroutine package, DLARTV subroutine 42—9 LAPACK subroutine package, DORGTR 42—8 LAPACK subroutine package, DORGTR subroutine 42—8 LAPACK subroutine package, DSBTRD subroutine 42—9 LAPACK subroutine package, DSTEBZ subroutine 42—15 LAPACK subroutine package, DSTEDC subroutine 42—14 LAPACK subroutine package, DSTEGR subroutine 42—17 LAPACK subroutine package, DSTEIN subroutine 42—15 LAPACK subroutine package, DSYEV subroutine 42—11 LAPACK subroutine package, DSYTRD 42—8 LAPACK subroutine package, DSYTRD subroutine 42—8 LAPACK subroutine package, equality-constrained least squares problems 75—6 to 75—7 LAPACK subroutine package, execution times 42—22 LAPACK subroutine package, fundamentals 75—1 to 75—2 LAPACK subroutine package, GEBAL subroutine 43—3 LAPACK subroutine package, GGBAK subroutine 43—7 LAPACK subroutine package, GGBAL subroutine 43—7 LAPACK subroutine package, GGHRD subroutine 43—7 LAPACK subroutine package, HSEQR subroutine 43—6 LAPACK subroutine package, least squares problems 75—4 to 75—7 LAPACK subroutine package, linear equality-constrained least squares problems 75—6 to 75—7 LAPACK subroutine package, linear least squares problems 75—4 to 75—6 LAPACK subroutine package, linear model problem 75—8 to 75—9 LAPACK subroutine package, linear system ofequations 75—2 to 75—4 LAPACK subroutine package, models 75—8 to 75—9 LAPACK subroutine package, nonsymmetric eigenproblems 75—17 to 75—20 LAPACK subroutine package, nonsymmetric eigenvalue problem 75—11 to 75—13 LAPACK subroutine package, singular value decomposition 75—13 to 75—15 75—20 LAPACK subroutine package, symmetric definite eigenproblems 75—15 to 75—17 LAPACK subroutine package, symmetric eigenvalue problem 75—9 to 75—11 LAPACK subroutine package, TGEVC subroutine 43—7 LAPACK subroutine package, TGSEN subroutine 43—7 LAPACK subroutine package, TGSNA subroutine 43—7 LAPACK subroutine package, TREVC subroutine 43—6 LAPACK subroutine package, TREXC subroutine 43—7 LAPACK subroutine package, tridiagonalization 42—8 LAPACK subroutine package, TRSEN subroutine 43—7 LAPACK subroutine package, TRSNA subroutine 43—7 Laplace expansion, determinantal relations 14—10 Laplace expansion, determinants 4—1 4—5 Laplace expansion, multiplication 13—18 to 13—19 Laplace expansion, permanents 31—2 Laplace expansion, permanents evaluation 31—12 Laplace transforms, frequency-domain analysis 57—6 Laplace transforms, LTI systems 57—14 Laplacian matrices, algebraic connectivity 36—1 36—2 Laplacian matrices, Fiedler vectors 36—7 36—8 Laplacian matrices, Hermitian matrices 8—5 Laplacian properties, algebraic connectivity 36—10 to 36—11 Laplacian properties, eigenvalues 28—7 Laplacian properties, graph parameters 28—9 28—10 Laplacian properties, graphs 28—8 to 28—9 Laplacian properties, matrix representations 28—7 Large-scale matrixcomputations, Arnoldi process 49—10 to 49—11 Large-scale matrixcomputations, dimension reduction 49—14 to 49—15 Large-scale matrixcomputations, eigenvalue computations 49—12 Large-scale matrixcomputations, fundamentals 49—1 to 49—2 Large-scale matrixcomputations, Krylov subspaces 49—5 to 49—6 Large-scale matrixcomputations, linear dynamical systems 49—14 to 49—15 Large-scale matrixcomputations, linear systems, equations 49—12 to 49—14 Large-scale matrixcomputations, nonsymmetric Lanczos process 49—8 to 49—10 Large-scale matrixcomputations, sparse matrix factorizations 49—2 to 49—5 Large-scale matrixcomputations, symmetric Lanczos process 49—6 to 49—7 Laser method 47—8 47—9 Last, Mathematica software, matrices manipulation 73—13 Last, Mathematica software, singular values 73—18 Last, Mathematica software, vectors 73—3 Latent semantic indexing (LSI) 63—3 to 63—5 Latin rectangle 31—6 Lawley-Hotelling trace statistic 53—13 LDPC (low density parity check) codes 61—11 LDU factorization 1—14 to 1—15 Leading diagonal 15—12 Leading dimension 74—2 Leading entry 1—7 Leading principle matrices 1—6 1—15 Leading principle minors, determinants 4—3 Leading principle minors, recognition and testing 21—7 Leading principle minors, stability 19—3 Leading principle submatrices 1—4 Leal Duarte, Antonio 34—1 to 34—15 Least squares algorithms 39—6 to 39—7 Least squares estimation, linear statistical models 52—8 Least squares estimation, multivariate statistical analysis 53—11 to 53—12 Least squares problems, fundamentals 5—14 to 5—16 Least squares problems, LAPACK subroutine package 75—4 to 75—7 Least squares problems, Matlab software 71—7 to 71—9 Least squares problems, numerical stability and instability 37—20 Least squares solutions, downdating 39—8 to 39—9 Least squares solutions, fundamentals 39—1 to 39—3 Least squares solutions, geometric aspects 39—4 to 39—5 Least squares solutions, linear systems, algebraic aspects 39—4 to 39—5 Least squares solutions, linear systems, algorithms 39—6 to 39—7 Least squares solutions, linear systems, damped least squares 39—9 to 39—10 Least squares solutions, linear systems, data fitting 39—3 to 39—4 Least squares solutions, orthogonal factorizations 39—5 to 39—6 Least squares solutions, QR factorization 39—8 to 39—9 Least squares solutions, rank revealing decompositions 39—11 to 39—12 Least squares solutions, sensitivity 39—7 to 39—8 Least squares solutions, updating 39—8 to 39—9 Lebesgue spaces 57—5 Lee and Seung algorithm 63—6 63—7 Left alternative algebra 69—10 Left alternative identities 69—2 Left deflating subspaces 55—7 left divide operator, Matlab software 71—7 Left eigenvector 4—6 Left Kronecker indices 55—7 Left Krylov subspace 49—8 Left Lanczos vectors 49—8 Left Moufang identity 69—10 Left multiplication operators 69—5 Left preconditioning, BiCGSTAB algorithm 41—12 Left preconditioning, Krylov subspaces and preconditioners 41—3 Left reducing subspaces 55—7 Left regular representation 68—2 Left singular space 45—1 Left singular vectors 5—10 45—1 Left-looking methods 40—10 Left-normalized product 69—16 Legs, simplexes 66—10 Length characteristics, Euclidean point space 66—2 Length characteristics, graphs 28—1 Length characteristics, max-plus algebra 25—2 Length characteristics, sign-pattern matrices 33—2 Length characteristics, stars 34—10 length command, Matlab software 71—2 71—9 Length of a walk, digraphs 29—2 Length of a walk, graphs 28—1 Length, Mathematica software, fundamentals 73—27 Length, Mathematica software, matrices 73—6 73—7 Length, Mathematica software, matrix algebra 73—12 Length, Mathematica software, vectors 73—3 73—4 Leon, Steven J. 71—1 to 71—22 Level characteristic 26—8 Levinson-Durbin algorithm 64—8 64—9 Levy — Desplanques theorem 14—6 Li, Chi-Kwong 18—1 to 18—11 Li, Ren-Cang 15—1 to 15—16 Lie algebras, angular momentum and representations 59—10 Lie algebras, fundamentals 70—1 to 70—3 Lie algebras, graded algebras 70—8 to 70—10 Lie algebras, modules 70—7 to 70—10 Lie algebras, nonassociative algebra 69—2 69—3 Lie algebras, semisimple algebras 70—3 to 70—7 Lie algebras, simple algebras 70—3 to 70—7 Lienard — Chipart Stability Criterion 19—4 Likelihood function 53—4 Likelihood ratio statistic 53—13 Limit set, chain recurrence 56—7 Limits, nonnegative and stochastic matrices 9—2 linalg package, Maple 72—1 Linder, David 72—21 Line graphs 28—4 Line, Mathematica software 73—5 Linear algebra, adjoints of linear operators 5—5 to 5—6 Linear algebra, annihilator 3—8 to 3—9 Linear algebra, bases 2—10 to 2—12 3—4 Linear algebra, change of basis 2—10 to 2—12 3—4 Linear algebra, coordinates 2—10 to 2—12 Linear algebra, determinants 4—1 to 4—6 Linear algebra, dimension theorem 2—6 to 2—9 Linear algebra, direct sum decompositions 2—4 to 2—6 Linear algebra, eigenvalues and eigenvectors 4—6 to 4—11 Linear algebra, Gauss — Jordan elimination 1—7 to 1—9 Linear algebra, Gaussian elimination 1—7 to 1—9 Linear algebra, Gram — Schmidt orthogonalization 5—8 to 5—10 Linear algebra, idempotence 2—12 Linear algebra, inner product spaces 5—1 to 5—3 5—5 Linear algebra, invariant subspaces 3—6 to 3—7
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