Àâòîðèçàöèÿ
Ïîèñê ïî óêàçàòåëÿì
Hogben L. — Handbook of Linear Algebra
Îáñóäèòå êíèãó íà íàó÷íîì ôîðóìå Íàøëè îïå÷àòêó?
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
Generalized Laplacian 36—10 to 36—11 Generalized least squares estimator 52—8 Generalized least squares problem 39—1 Generalized line graphs 28—4 Generalized Minimal Residual (GMRES), convergence rates 41—15 to 41—16 Generalized Minimal Residual (GMRES), Krylov space methods 41—7 41—9 Generalized Minimal Residual (GMRES), linear systems of equations 49—13 Generalized Minimal Residual (GMRES), matrices function behavior 16—11 Generalized Minimal Residual (GMRES), preconditioners 41—12 Generalized octonions 69—4 Generalized quarternions 69—4 Generalized Schur complement 52—4 Generalized sign pattern 33—2 Generalized Singleton bound 61—12 Generalized singular value decomposition (GSVD) 15—12 Generalized stars 34—10 to 34—14 Generalized variance 52—3 Generator matrix, convolutional codes 61—11 Generator matrix, linear block codes 61—3 Generators, certain integral domains 23—2 Generators, linear independence and rank 25—12 Generators, polynomial 61—7 Geometry and geometric aspects, affine spaces 65—1 to 65—4 Geometry and geometric aspects, eigenvalues and eigenvectors 4—6 Geometry and geometric aspects, Euclidean geometry 66—1 to 66—15 Geometry and geometric aspects, Euclidean spaces 65—4 to 65—6 Geometry and geometric aspects, fundamentals 65—1 Geometry and geometric aspects, least squares solutions 39—4 to 39—5 Geometry and geometric aspects, linear programming 50—13 Geometry and geometric aspects, matrix power asymptotics 25—8 Geometry and geometric aspects, max-plus eigenproblem 25—6 Geometry and geometric aspects, nonnegative and stochastic matrices 9—2 Geometry and geometric aspects, projective spaces 65—6 to 65—9 Geometry and geometric aspects, semidefinite programming 51—5 Geometry’ Rotations’ package, Mathematica software 73—4 Gerhard, Jurgen 72—21 Gersgorin discs 14—5 to 14—7 Gersgorin theorem, generalized cycle products 29—5 Gersgorin theorem, pseudospectra 16—3 GGBAK LAPACK subroutine 43—7 GGBAL LAPACK subroutine 43—7 GGHRD LAPACK subroutine 43—7 GIEP (General Inverse Eigenvalue Problem) 34—8 Gilbert Varshamov bound, linear code classes 61—10 Gilbert Varshamov bound, main linear coding problem 61—6 Givens algorithm 46—5 to 46—6 givens function, Matlab software 42—9 Givens QR factorization 38—14 Givens rotations, orthogonalization 38—13 to 38—14 Givens rotations, QR factorization 39—9 Givens rotations, tridiagonalization 42—5 42—7 Givens transformation 38—13 Glide reflection 65—5 Global invariant manifolds 56—19 Glossary G—1 to G—40 GMRES (Generalized Minimal Residual), convergence rates 41—15 to 41—16 GMRES (Generalized Minimal Residual), Krylov space methods 41—7 41—9 GMRES (Generalized Minimal Residual), linear systems of equations 49—13 GMRES (Generalized Minimal Residual), matrices function behavior 16—11 GMRES (Generalized Minimal Residual), preconditioners 41—12 Golay codes 61—8 Goldman — Tucker theorem 51—6 Golub — Kahan singular value decomposition 45—6 Golub — Reinsch singular value decomposition 45—6 Gondran — Minoux properties 25—12 25—13 Google (search engine), information retrieval 63—10 to 63—14 Google (search engine), Markov chains 54—4 to 54—5 Google (search engine), PageRank 63—11 Google (search engine), Web search 63—9 Goppa code, algebraic geometric 61—10 grad, Mathematica software 73—15 73—16 Graded algebras 70—8 to 70—10 Grading, eigenvalue problems 15—13 Grading, Krylov subspaces 49—6 Grading, polar decomposition 15—8 Grading, singular value problems 15—15 Grading, tensor algebras 13—20 to 13—22 Gradual underflow 37—11 to 37—12 Gragg studies 44—4 Graham-Pollak theorem 30—9 Gram matrices, Euclidean geometry 66—5 to 66—7 Gram matrices, Hermitian matrices 8—1 8—2 Gram — Schmidt calculation, Maple software 72—6 Gram — Schmidt methods, Arnoldi factorization 44—3 to 44—4 Gram — Schmidt methods, unitary similarity 7—2 7—4 Gram — Schmidt orthogonalization 5—8 to 5—10 Gram — Scmidt, Mathematica software 73—4 Gramian, Euclidean simplexes 66—8 graphical user interfaces (GUIs) 71—19 to 71—22 Graphics, Matlab software 71—14 to 71—17 Graphics’ Arrow’, Mathematica software 73—5 graphs see «Algebraic connectivity» «Euclidean specific Graphs, adjacency matrix 28—5 to 28—7 Graphs, association schemes 28—11 to 28—12 Graphs, doubly stochastic matrices 27—10 Graphs, eigenvalues 28—5 to 28—7 Graphs, fundamentals 28—1 to 28—3 Graphs, matrix completion problems 35—2 Graphs, matrix representations 28—7 to 28—9 Graphs, modeling and analyzing fill 40—11 Graphs, multiplicative D-stability 19—6 Graphs, multiplicities and parter vertices 34—2 Graphs, parameters 28—9 to 28—11 Graphs, simplexes 66—10 Graphs, special types 28—3 to 28—5 Grassmann characteristics, dynamical systems 56—9 to 56—11 Grassmann characteristics, Floquet theory 56—13 Grassmann characteristics, manifolds, dynamical systems 56—7 Grassmann characteristics, matrix pair 15—12 Grassmann characteristics, tensor algebras 13—21 Grassmann characteristics, tensors 13—12 to 13—17 Grassmann, Taksar, Heyman (GTH) trick 54—13 Gray Code order 31—12 Greatest common divisor domain (GCDD) 23—2 Greatest common divisors 23—2 Greatest integer function P—3 Greenbaum, Anne 41—1 to 41—17 Green’s functions 59—10 to 59—11 Griesmer bound 61—5 Grobman — Hartman theorem 56—20 Group P—3 to P—4 Group inverse 9—2 Group of invertible linear operators 67—1 Group representations, character table 68—6 to 68—8 Group representations, characters 68—5 to 68—6 Group representations, fundamentals 68—1 to 68—3 Group representations, induction of characters 68—8 to 68—10 Group representations, matrix representations 68—3 to 68—5 Group representations, orthogonality relations 68—6 to 68—8 Group representations, restriction of characters 68—8 to 68—10 Group representations, symmetric group representations 68—10 to 68—11 Group ring 68—2 Grover’s search algorithm 62—15 to 62—17 GSVD see «Generalized singular value decomposition (GSVD)» GTH (Grassmann, Taksar, Heyman) trick 54—13 GUI see «Graphical user interfaces (GUIs)» Gunaratne, Ajith 60—13 H-matrices 19—9 Hacjan studies 50—23 Hadamard inequalities, determinantal relations 14—11 Hadamard inequalities, inequalities 17—11 Hadamard matrix, nonsquare case 32—5 Hadamard matrix, permanents 31—8 Hadamard matrix, square case 32—2 Hadamard product, complex sign and ray patterns 33—14 Hadamard product, positive definite matrices 8—9 Hadamard product, rank and nullity 14—14 Hadamard product, square matrices 27—4 Hadamard product, totally positive and negative matrices 21—10 21—11 Hadamard — Fischer inequality 8—10 Hadamard’s determinantal inequality 8—10 8—11 Haemers, Willem H. 28—1 to 28—12 Half-line subset 13—24 Halfspaces 25—11 Hall matrices 27—3 27—4 Hall, Frank J. 33—1 to 33—17 Hamilton cycle 28—1 Hamilton-Jacobi partial differential equations 25—6 Hamiltonian operator 59—2 Hamiltonian system 56—13 Hamiltonian, minimally chordal symmetric 35—15 Hamming association scheme 28—12 Hamming properties, code 61—6 61—9 Hamming properties, distance 61—2 Hamming properties, weight 61—2 Han, Lixing 5—1 to 5—16 Hankel matrices, Maple software 72—18 Hankel matrices, structured matrices 48—2 48—3 Hankel matrices, totally positive and negative matrices 21—12 HankelMatrix, Mathematica software 73—6 Hansen, Per Christian 39—1 to 39—12 Hard constraints 51—1 Hardware floats, Maple software 72—14 Hardy space 57—5 Hardy, Littlewood, Polya theorem 27—11 Hare, Dave 72—21 Hartman-Grobman theorem 56—20 Hat matrix 52—9 Hautus-Popov test 57—8 Heat equation 59—11 Heat kernel 59—11 Height characteristic 9—7 26—8 Hentzel, Irvin 69—25 Hereditary 35—2 Hermite normal form 23—5 to 23—7 23—6 Hermitian characteristics, angular momentum and Hermitian characteristics, representations 59—9 Hermitian characteristics, Arnoldi factorization 44—3 Hermitian characteristics, classical groups 67—5 Hermitian characteristics, differential equations 55—11 Hermitian characteristics, differential-algebraic equations 55—15 Hermitian characteristics, extensions 16—13 Hermitian characteristics, iterative solution methods 41—4 to 41—7 Hermitian characteristics, Jordan algebras 69—13 Hermitian characteristics, products 10—9 Hermitian characteristics, Schrodinger’s equation 59—7 59—8 Hermitian characteristics, Schur complements 10—7 Hermitian characteristics, splitting theorems and stability 26—14 Hermitian forms 12—7 to 12—9 Hermitian matrices, adjoint 1—4 Hermitian matrices, adjoint operators 5—6 Hermitian matrices, Arnoldi process 49—10 Hermitian matrices, bilinear forms 12—7 to 12—9 Hermitian matrices, eigenvalues 8—3 to 8—5 15—5 Hermitian matrices, fundamentals 1—4 8—1 Hermitian matrices, inertia 19—2 Hermitian matrices, multiplicities and Parter vertices 34—2 Hermitian matrices, numerical range 18—6 Hermitian matrices, order properties, eigenvalues 8—3 to 8—5 Hermitian matrices, positive definite and semidefinite matrices 35—8 Hermitian matrices, positive definite characteristics 5—2 Hermitian matrices, pseudo-inverse 5—12 Hermitian matrices, relative perturbation theory 15—14 Hermitian matrices, singular value decomposition 5—11 Hermitian matrices, singular values 17—2 17—13 Hermitian matrices, sparse matrices 49—4 to 49—5 Hermitian matrices, spectral theory 7—5 7—8 Hermitian matrices, standard linear preserver problems 22—5 Hermitian matrices, submatrices and block matrices 10—2 Hermitian matrices, symmetric factorizations 38—15 Hermitian positive definite and semidefinite, ARPACK 76—7 to 76—8 Hermitian preconditioning 41—3 Hermitian properties, linear operators 5—5 Hermitian properties, pencils 24—6 Hermitian properties, property L 24—6 HermitianTranspose, Maple software 72—3 72—5 Hershkowitz, Daniel 19—1 to 19—10 hes, Mathematica software 73—16 Hessenberg pattern 33—3 33—4 HessenbergDecomposition, Mathematica software 73—19 73—27 Hessian properties, Hermitian matrices 8—2 Hessian properties, semidefinite programming 51—10 Hestenes studies 46—2 Hidden constraint 51—10 High relative accuracy bidiagonal singular value decomposition 45—7 45—8 High relative accuracy, eigenvalues and singular values, accuracy 46—2 to 46—5 46—7 High relative accuracy, eigenvalues and singular values, fundamentals 46—1 to 46—2 High relative accuracy, eigenvalues and singular values, one-sided Jacobi SVD algorithm 46—2 to 46—5 High relative accuracy, eigenvalues and singular values, positive definite matrices 46—10 to 46—14 High relative accuracy, eigenvalues and singular values, preconditioned Jacobi SVD algorithm 46—5 to 46—7 High relative accuracy, eigenvalues and singular values, rank revealing decomposition 46—7 to 46—10 High relative accuracy, eigenvalues and singular values, structured matrices 46—7 to 46—10 High relative accuracy, eigenvalues and singular values, symmetric indefinite matrices 46—14 to 46—16 Higham and Tisseur studies 16—12 Higham, Nicholas J. 11—1 to 11—12 Highest weight vector 70—7 hilb command, Matlab software 71—18 Hilbert matrix, linear systems conditioning 37—11 Hilbert matrix, preconditioned Jacobi SVD algorithm 46—7 Hilbert matrix, rank revealing decomposition 46—10 Hilbert spaces, quantum computation 62—2 Hilbert spaces, random signals 64—4 Hilbert spaces, Schrodinger’s equation 59—7 Hilbert-Schmidt inner product 13—23 13—24 HilbertMatrix, Mathematica software, matrices 73—6 HilbertMatrix, Mathematica software, singular values 73—18 Hill’s equation 56—14 Hirsch and Bendixson inequalities 14—2 HITS (Hypertext Induced Topic Search) 63—9 HKM method 51—8 Hodge star operator 13—24 to 13—26 Hoffman polynomial 28—5 28—6 Hoffman-Wielandt inequality 7—7 Hoffman-Wielandt theorem 15—2 Hogben, Leslie 6—1 to 6—14 35—1 Holder inequality 37—3 Holder norm 37—2 Holmes, Randall R. 68—1 to 68—11 Homogeneity, cone programming 51—2 Homogeneity, coordinates 65—7 Homogeneity, differential equation 2—3 2—4 Homogeneity, Euclidean simplexes 66—8 Homogeneity, function field, linear code classes 61—10 Homogeneity, line coordinates 65—7 Homogeneity, linear differential equations 55—2 Homogeneity, Markov chains 54—1 Homogeneity, partial inverse M-matrices 35—14 Homogeneity, pencil strict equivalence 23—9 Homogeneity, polynomials 23—2 23—9 Homogeneity, projective spaces 65—7 Homogeneity, systems of linear equations 1—9 1—10 Homogeneity, tensor algebras 13—21 Homogeneity, vector norms 37—2 Homogeneity, vector seminorms 37—3 Homogeneous ofdegree 13—21 Homomorphism, bimodules 69—6 Homomorphism, modules 70—7 Homomorphism, nonassociative algebra 69—3 Homotopy approach 20—12 Hopfalgebra 69—18 Horn inequalities 14—9 Hotelling studies 32—1 Hotelling’s distribution 53—9 53—10 Householder method, algorithm efficiency 37—17 Householder method, singular value decomposition 45—5 Householder properties, algorithm 46—5 to 46—6 Householder properties, QR factorization 38—13 Householder properties, reduction, bidiagonal form 45—5 Householder properties, transformation 38—13 Householder properties, vectors 38—13 Householder reflections, orthogonalization 38—13 38—15
Ðåêëàìà
|
|
Î ïðîåêòå