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
Simple events 52—2 Simple graphs, algebraic connectivity 36—1 to 36—4 36—9 Simple graphs, graphs 28—1 simple linear regression 52—8 Simple row operations 23—6 Simple walk 29—2 Simplex method 50—11 to 50—13 Simplexes 66—7 to 66—13 Simplicial cones 26—4 simplify, Maple software 72—8 Simplify, Mathematica software, eigenvalues 73—15 73—16 Simplify, Mathematica software, fundamentals 73—25 Simplify, Mathematica software, matrix algebra 73—12 Simultaneous similarity, classification I 24—7 to 24—10 Simultaneous similarity, classification II 24—10 to 24—11 Simultaneous similarity, fundamentals 24—5 to 24—6 Sin, Mathematica software 73—26 Sine, function computation methods 11—11 Single precision 37—13 Single-input, single-output, time-invariant linear dynamical system 49—14 Singleton bound, convolutional codes 61—12 Singleton bound, linear block codes 61—5 Singular matrices 1—12 Singular pencils, generalized eigenvalue problem 43—2 Singular pencils, linear differential-algebraic equations 55—7 Singular value decomposition (SVD), accuracy 46—2 to 46—5 46—7 Singular value decomposition (SVD), algorithms 45—4 to 45—12 Singular value decomposition (SVD), fundamentals 5—10 to 5—12 45—1 Singular value decomposition (SVD), LAPACK subroutine package 75—13 to 75—15 75—20 Singular value decomposition (SVD), numerical stability and Singular value decomposition (SVD), instability 37—20 Singular value decomposition (SVD), orthogonal factorizations 39—5 Singular value vector 17—1 Singular values and singular value inequalities, characterizations 17—1 to 17—3 Singular values and singular value inequalities, eigenvalues, Hermitian matrices 17—13 to 17—14 Singular values and singular value inequalities, fundamentals 17—1 to 17—3 Singular values and singular value inequalities, general matrices 17—13 to 17—14 Singular values and singular value inequalities, generalizations 17—14 to 17—15 Singular values and singular value inequalities, inequalities 17—7 to 17—12 Singular values and singular value inequalities, matrix approximation 17—12 to 17—13 Singular values and singular value inequalities, results 17—14 to 17—15 Singular values and singular value inequalities, special matrices 17—3 to 17—5 Singular values and singular value inequalities, unitarily invariant norms 17—5 to 17—7 Singular values, high relative accuracy, accurate SVD 46—2 to 46—5 46—7 Singular values, high relative accuracy, fundamentals 46—1 to 46—2 Singular values, high relative accuracy, one-sided Jacobi SVD algorithm 46—2 to 46—5 Singular values, high relative accuracy, positive definite matrices 46—10 to 46—14 Singular values, high relative accuracy, preconditioned Jacobi Singular values, high relative accuracy, SVD algorithm 46—5 to 46—7 Singular values, high relative accuracy, rank revealing decomposition 46—7 to 46—10 Singular values, high relative accuracy, structured matrices 46—7 to 46—10 Singular values, high relative accuracy, symmetric indefinite matrices 46—14 to 46—16 Singular values, inequalities 17—7 to 17—8 17—9 17—10 Singular values, Mathematica software 73—16 to 73—18 Singular values, matrix equalities and inequalities 14—8 to 14—10 Singular values, problems, generalized 15—12 to 15—13 Singular values, problems, perturbation theory 15—6 to 15—7 15—12 Singular values, problems, relative perturbation theory 15—15 to 15—16 Singular values, singular value decomposition 5—10 Singular-triplet 15—6 Singularity, isomorphism 3—7 SingularValueDecomposition, Mathematica software, decomposition 73—18 SingularValueDecomposition, Mathematica software, fundamentals 73—27 SingularValueDecomposition, Mathematica software, singular values 73—17 SingularValueList, Mathematica software, fundamentals 73—27 SingularValueList, Mathematica software, matrix algebra 73—11 SingularValueList, Mathematica software, singular values 73—16 SingularValues, Maple software 72—9 SingularValues, Mathematica software 73—27 Sinusoids in noise 64—14 size command, Matlab software 71—2 Size, matrices 1—3 Skeel condition number 38—2 Skeel matrix condition number 38—2 Skew product flows, linear 56—11 to 56—12 Skew — Hermitian characteristics, matrices 1—4 1—6 Skew — Hermitian characteristics, spectral theory 7—5 7—8 Skew-component 56—11 Skew-symmetric matrices, direct sum decompositions 2—5 Skew-symmetric matrices, fundamentals 1—4 1—6 Skew-symmetric matrices, invariance 3—7 Skew-symmetric matrices, kernel and range 3—6 Slack variables, linear programming 50—7 Slack variables, linear programs 50—8 Slackness, duality 50—14 51—6 Slackness, max-plus eigenproblem 25—7 Slackness, optimality conditions 51—6 Slapnicar, Ivan 42—1 to 42—22 Slater’s Constraint Qualification 51—7 51—8 Small oscillations 59—4 Smith invariant factors, rational canonical form 6—13 Smith invariant factors, Smith normal form 6—11 Smith normal form, canonical forms 6—11 to 6—12 Smith normal form, matrix equivalence 23—5 to 23—8 23—6 Smith normal matrix 6—11 SmithForm, Maple software 72—16 Smooth curve 61—10 Smooth point 24—8 Soft information 61—10 Software see specific package Software, freeware 77—1 to 77—3 Software, pseudo-spectra computation 16—12 sol, Mathematica software 73—21 73—23 Solution perturbation, linear system perturbations 38—2 Solution set 1—9 Solutions, linear differential equations 55—2 Solutions, matrix, inverse eigenvalue problems 20—1 Solutions, systems oflinear equations 1—9 Solvability index 69—5 Solvability, general properties 69—5 Solvability, semisimple and simple algebras 70—3 Solvable radical algebras 69—6 Solve, Mathematica software, eigenvalues 73—14 Solve, Mathematica software, linear systems 73—20 73—21 73—23 SOR (successive overrelaxation) methods 41—3 to 41—4 Sorenson, D.C. 44—1 to 44—12 76—1 Spacing, Fourier analysis 58—3 Spacing, functional and discrete theories 58—12 Span, linear independence 2—1 to 2—3 Span, span and linear independence 2—1 Spanning family 25—2 Spanning subgraphs 28—2 Spanning tree 28—2 Spans, max-plus algebra 25—2 Spare matrices, fundamentals 43—1 Spare matrices, Matlab software 71—9 to 71—11 SPARFUN directory, Matlab software 71—10 Sparity pattern 46—8 Sparse approximate inverse 41—11 Sparse Cholesky factorization 49—3 Sparse direct solvers 77—2 Sparse eigenvalue solvers 77—2 Sparse iterative solvers 77—3 Sparse LU factorization 49—3 Sparse matrices, analyzing fill 40—10 to 40—13 Sparse matrices, effect of reorderings 40—14 to 40—18 Sparse matrices, factorizations 40—4 to 40—10 Sparse matrices, fundamentals 40—1 to 40—2 Sparse matrices, Lanczos methods 42—21 Sparse matrices, large-scale matrix computations 49—2 Sparse matrices, modeling 40—10 to 40—13 Sparse matrices, reordering effect 40—14 to 40—18 Sparse matrices, sparse matrices 40—2 to 40—4 Sparse matrices, unsymmetric matrix eigensvalue techniques 43—9 to 43—11 Sparse matrix factorizations 49—2 to 49—5 Sparse nonsymmetric matrices, modeling and analyzing fill 40—11 Sparse nonsymmetric matrices, reordering effect 40—15 40—17 Sparse symmetric positive definite matrices 40—15 Sparse triangular solve 49—3 SparseArray, Mathematica software 73—6 73—8 73—9 Sparsity pattern 9—21 Sparsity structure 40—4 Special boundary points 18—3 to 18—4 Special gate 62—7 Special linear group 67—3 Special matrices, Matlab software 71—5 to 71—7 Special unitary group 67—6 Special, Jordan algebra 69—12 Special-purpose indices 63—9 Specialty problem 69—17 Spectra, nonnegative IEPs 20—6 to 20—10 Spectral absolute value 17—1 Spectral cones 26—8 Spectral Conjecture 20—7 Spectral density 64—5 Spectral estimation 64—14 to 64—15 Spectral factorization 64—5 Spectral norm, matrix norms 37—4 Spectral norm, unitarily invariant norms 17—6 Spectral norm, unitary similarity 7—2 Spectral pair 26—9 Spectral projections 55—8 Spectral projector 25—8 Spectral properties 21—8 Spectral radius, eigenvalues and eigenvectors 4—6 Spectral radius, reducible matrices 9—10 Spectral Theorem, Hermitian matrices 8—2 Spectral Theorem, spectral theory 7—5 to 7—6 Spectral theory, cone invariant departure, matrices 26—8 to 26—10 Spectral theory, matrices, special properties 7—5 to 7—9 Spectral transformations, ARPACK 76—7 76—8 Spectral transformations, implicitly restarted Arnoldi method 44—11 to 44—12 Spectral value set 16—12 Spectrally arbitrary pattern (SAP) 33—11 Spectrum localization 14—5 to 14—8 Spectrum of reducible matrices 25—7 Spectrum, adjacency matrix 28—5 Spectrum, eigenvalues and eigenvectors 4—6 Spectrum, numerical range 18—3 to 18—4 Speed, methods comparison 42—21 Sphere-packing bound 61—5 Spin-factor 69—13 Split composition algebras 69—8 Split null extension 69—6 Split quasi-associative algebras 69—16 Splitting theorems 26—13 to 26—14 spy command, Matlab software 71—10 Sqrt, Mathematica software 73—17 73—26 Square case 32—2 to 32—4 Square complex matrix 19—3 Square linear system solution 1—14 Square matrices, combinatorial matrix theory 27—3 to 27—6 Square matrices, fundamentals 1—3 1—4 Square matrices, nonsingularity characteristics 2—9 to 2—10 Square matrices, stability 19—3 19—5 19—9 Square root, matrices 11—4 to 11—5 Squared multiple correlation 52—8 Squareroot-free method 45—5 SRRD see «Symmetric rank revealing decomposition (SRRD)» SRT see «Standard row tableaux (SRT)» SSYEV, driver routine 75—10 to 75—11 SSYGV, driver routine 75—16 to 75—17 Stability and inertia, additive D-stability 19—7 to 19—8 Stability and inertia, fundamentals 19—1 to 19—2 Stability and inertia, inertia 19—2 to 19—3 Stability and inertia, Lyapunov diagonal stability 19—9 to 19—10 Stability and inertia, multiplicative D-stability 19—5 to 19—7 Stability and inertia, stability 19—3 to 19—5 Stability, cone invariant departure, matrices 26—13 to 26—14 Stability, error analysis 37—18 to 37—21 Stability, group representations 68—1 Stability, linear differential-algebraic equations 55—14 to 55—16 Stability, linear ordinary differential equations 55—10 to 55—14 Stability, LTI systems 57—7 Stability, matrices, Maple software 72—20 to 72—21 Stability, matrix stability and inertia 19—3 to 19—5 Stability, pseudo-spectra 16—2 Stability, sign pattern matrices 33—7 Stability, sign-pattern matrices 33—7 to 33—9 Stability, signal processing 64—2 Stability, subspaces, linear differential equations 56—3 Staircase form 57—9 Standard basis 2—3 Standard column tableau (SCT) 50—13 Standard deviations, random vectors 52—3 Standard deviations, statistics and random variables 52—2 Standard forms, linear preserver problems 22—2 to 22—4 Standard forms, linear programming 50—7 50—7 Standard forms, singular value decomposition 45—1 Standard inner product 5—2 13—23 Standard linear preserver problems 22—4 to 22—7 Standard map 22—2 Standard matrix 3—3 Standard row tableaux (SRT) 50—8 to 50—10 Standardized population principal component 53—5 Star-shaped sets 20—6 Stars, multiplicity lists 34—10 to 34—14 Starting vector, ARPACK 76—6 stat, Mathematica software 73—15 73—16 State, classification 54—7 to 54—9 State, equation, control theory 57—2 State, estimation, control theory 57—11 to 57—13 State, feedback 57—2 57—7 57—13 State, observer 57—12 State, space 54—1 57—2 State, stochastic and substochastic matrices 9—15 State, variables 49—14 State, vectors 4—10 57—2 State-space dimension 49—14 State-space transformations, frequency-domain analysis 57—6 State-space transformations, LTI systems 57—7 Static feedback 57—13 Stationary characteristics 64—4 to 65—5 Stationary distribution, Markov chain 54—2 Stationary distribution, stochastic and substochastic matrices 9—15 Statistical independence 53—2 Statistical inference 53—12 to 53—13 Statistics see «Probability and statistics applications» Steady state vector 4—10 Steady-state flux cone 60—10 Steady-state flux equation 60—10 Stein studies 26—14 Stewart studies 44—4 Stewart, Michael 64—1 to 64—18 Stochastic and substochastic matrices 9—15 to 9—17 Stochastic hyperlink matrix 63—11 Stochastic spectral estimation 64—14 Stoichiometric coefficient 60—10 Stoichiometry matrix 60—10 Stopping criteria 41—16 to 41—17 Stopping criterion, ARPACK 76—6 Stopping matrices 9—15 Storage declaration, ARPACK 76—5 to 76—6 Strassen, V. 47—8 Strassen’s algorithm 47—3 47—4 Strassen’s formula 47—3 Strategies, matrix games 50—18 Stratification 24—8 Strengthened Landau inequalities 27—9 Strict column signing 33—5 Strict complementarity 51—6 Strict equivalence, pencils, generalized eigenvalue problem 43—2 Strict equivalence, pencils, matrices over integral domains 23—9 to 23—10 Strict row signing 33—5 Strict signing 33—5 Strictly block lower triangular matrices 10—4 Strictly block upper triangular matrices 10—4 Strictly copositive matrices 35—11 to 35—12 Strictly diagonally dominant matrices 9—17 Strictly similarity 24—5 Strictly unitarily equivalence 43—2 Strictly upper triangular matrices 10—4
Ðåêëàìà
|
|
Î ïðîåêòå