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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
Restarting process 44—4 to 44—5 Restricted subspace dimensions 44—10 Retrieved documents 63—2 Reverse communication 76—2 Reverse, Mathematica software 73—27 rhs, Mathematica software 73—20 Riccatti equation 51—9 Ridge aggression 39—9 Rigal — Gaches theorem 38—3 Right alternative algebras 69—10 69—14 Right alternative identities 69—2 Right deflating subspaces 55—7 Right divide operator, Matlab software 71—7 Right Kronecker indices 55—7 Right Krylov subspace, Arnoldi process 49—10 Right Krylov subspace, nonsymmetric Lanczos process 49—8 Right Lanczos vectors 49—8 Right Moufang identity 69—10 Right multiplication operators 69—5 Right nilpotency 69—14 Right preconditioning 41—3 Right reducing subspaces 55—7 Right simplexes 66—10 Right singular space 45—1 Right singular vectors 45—1 Right-looking methods 40—10 Rigid motion 65—4 Ring P—6 Ring automorphism 22—7 Ritz pairs, Arnoldi factorization 44—3 Ritz pairs, spare matrices 43—10 Ritz values, implicit restarting 44—8 Ritz values, Krylov subspace projection 44—2 Ritz values, spare matrices 43—10 Ritz vectors, Krylov subspace projection 44—2 Ritz vectors, polynomial restarting 44—6 Ritz vectors, spare matrices 43—10 RLS (recursive least squares) 64—12 RMSD (root-mean-square deviation) 60—4 to 60—7 Robinson, J. 50—24 Robust linear systems, dynamical systems 56—16 to 56—19 Robust linear systems, linear skew product flows 56—12 Robust representations 42—15 to 42—17 Romani, R. 47—8 Rook numbers 31—10 Rook polynomials 31—10 to 31—11 Root space 70—4 Root system 70—4 Root, positive definite matrices 8—6 Root-mean-square deviation (RMSD) 60—4 to 60—7 RootOf, Maple software 72—11 72—20 roots function, Matlab software 72—16 Rosenthal, Joachim 61—1 to 61—13 Rosette 29—13 RotateLeft, Mathematica software 73—13 RotateRight, Mathematica software 73—13 Rotation group, representations 59—9 to 59—10 Rotation matrix 65—5 Rothblum index theorem 26—8 26—10 Rothblum, Uriel G. 9—1 to 9—23 Round-robin tournament 27—9 Round-to-nearest standard 37—12 Rounding error bounds 37—14 Rounding errors 37—12 see Rounding mode 37—12 Routh — Hurwitz matrices, stability 19—3 Routh — Hurwitz matrices, totally positive and negative matrices 21—3 to 21—4 Routh-Hurwitz StabilityCriterion 19—4 Row cyclic pivoting strategy 42—18 Row echelon form (REF) 1—7 Row-cyclic pivoting strategy 42—18 Row-echelon form 38—7 Row-stochastic matrices 9—15 RowReduce, Mathematica software, linear systems 73—20 73—23 RowReduce, Mathematica software, matrix algebra 73—10 73—12 Rows, balanced signing 33—5 Rows, equivalence 1—7 23—5 Rows, feasibility 50—8 Rows, indices 23—9 Rows, matrices 1—3 Rows, pivoting 46—5 Rows, rank 25—13 Rows, row-major format 74—2 Rows, scaling 9—20 Rows, sign solvability 33—5 Rows, spaces 2—6 Rows, sum vectors 27—7 Rows, vectors 1—3 Roy’s maximum root statistic 53—13 RRD see «Rank revealing decomposition (RRD)» RREF see «Reduced row echelon form (RREF)» rref command, Matlab software 71—17 RRQR (rank revealing QR) decomposition 39—11 Ruskeepaa, Heikki 73—1 to 73—27 Ryser/Nijenhius/Wilf (RNW) algorithm 31—12 S-matrices, sign-pattern matrices 33—5 to 33—7 Sabinin algebra 69—16 to 69—17 Saddle point 50—18 Sadun, Lorenzo 59—1 to 59—11 Saiago, Carlos M. 34—1 to 34—15 Sample canonical correlations and variates 53—8 Sample correlation coefficient 52—9 Sample covariance matrix 53—8 Sample mean 53—4 Sample points 52—2 Sample principal components 53—5 Sample spaces 52—2 Samples, statistics and random variables 52—2 Sampling, functional and discrete theories 58—12 Sandwich theorem 28—10 SAP (spectrally arbitrary pattern) 33—11 Saturation digraphs 25—6 25—7 Scalar matrix 1—4 Scalar multiple, vector spaces 3—2 Scalar multiplication, matrices 1—3 Scalar multiplication, vector spaces 1—1 Scalar transformation 3—2 Scaled sampling 58—12 Scaling, doubly stochastic matrices 27—10 Scaling, nonnegative matrices 9—20 to 9—23 Schatten-p norms 17—5 Schein rank 25—13 Schlaefli simplexes 66—10 66—11 66—12 Schneider, Barker and, studies 26—3 Schneider, Hans 26—1 to 26—14 Schneider’s theorem 14—3 Schoenberg characteristics 66—8 Schoenberg transform 35—10 Schoenberg’s variation diminishing property 21—10 Schonhage, A. 47—8 Schrodinger’s equation 59—2 59—6 Schur algorithm 64—8 Schur complements, bipartite graphs 30—6 to 30—7 Schur complements, determinants 4—3 4—4 4—5 Schur complements, inverse identities 14—15 Schur complements, partitioned matrices 10—6 to 10—8 Schur complements, random vectors 52—4 52—5 Schur complements, symmetric indefinite matrices 46—16 Schur decomposition, function computation methods 11—11 Schur decomposition, implicit restarting 44—6 Schur decomposition, pseudospectra 16—3 Schur properties, basis 44—6 Schur properties, form 16—11 Schur properties, inequalities 14—2 68—11 Schur properties, linear prediction 64—8 Schur properties, product 8—9 Schur properties, relations 68—4 Schur properties, spectral estimation 64—15 Schur — Horn theorem 20—1 to 20—2 SchurDecomposition, Mathematica software 73—19 Schur’s lemma 68—2 Schur’s theorem, eigenvalue problem 43—2 Schur’s theorem, unitary similarity 7—5 Schur’s Triangularization theorem 10—5 Scilab’s Maxplus toolbox 25—6 Score vector 27—9 Scores, estimation 53—8 SCT see «Standard column tableau (SCT)» SDP see «Semidefinite programming (SDP)» Search engines, Markov chains 54—4 to 54—5 see Seber, George A.F. 53—1 to 53—14 Second canonical correlations and variates 53—7 Segment, Euclidean point space 66—2 Seidel matrix 28—8 Seidel switching, graphs 28—9 Seidel switching, matrix representations 28—8 Self-adjoints, Hermitian matrices 8—1 Self-adjoints, linear operators 5—5 Self-adjoints, Schrodinger’s equation 59—7 Self-dual code 61—3 Self-inverse sign pattern 33—3 Self-polar cone 51—5 Semantic indexing, latent 63—3 to 63—5 Semiaffine characteristics 65—2 Semicolon, Maple software 72—2 Semiconvergence, numerical methods 54—12 Semiconvergence, reducible matrices 9—8 9—11 Semidefinite programming (SDP), applications 51—9 to 51—11 Semidefinite programming (SDP), constraint qualification 51—7 Semidefinite programming (SDP), duality 51—5 to 51—7 Semidefinite programming (SDP), fundamentals 51—1 to 51—3 Semidefinite programming (SDP), geometry 51—5 Semidefinite programming (SDP), notation 51—3 to 51—5 Semidefinite programming (SDP), optimality conditions 51—5 to 51—7 Semidefinite programming (SDP), primal-dual interior point algorithm 51—8 to 51—9 Semidefinite programming (SDP), results 51—3 to 51—5 Semidefinite programming (SDP), strong duality 51—7 Semidistinguished face 26—8 Semimodules 25—2 Semipositive basis 26—8 Semipositive Jordan basis 26—8 Semipositive Jordan chain 26—8 Semipositives, fundamentals 9—2 Semipositives, Perron — Frobenius theorem 26—2 Semisimple algebras, general properties 69—4 69—5 Semisimple algebras, Lie algebras 70—3 to 70—7 Semisimple eigenvalues 4—6 Semistable matrices 19—9 Semrl, Peter 22—1 to 22—8 Sensitivity, least squares solutions 39—7 to 39—8 Sensitivity, linear programming 50—17 to 50—18 Separation theorem 25—11 Separation, alternative algebras 69—10 Separation, eigenvalue problems 15—2 Separator, reordering effect 40—16 Sesquilinear forms 12—1 12—6 Sets, nonnegative matrices 9—23 Setting up linear programs 50—3 to 50—7 Severin, Andrew 60—13 SGEEV, driver routine 75—11 to 75—13 SGELS driver routine 75—5 to 75—6 SGESV driver routine 75—3 to 75—4 SGESVD, driver routine 75—14 to 75—15 SGGEV, driver routine 75—18 to 75—20 SGGGLM, driver routine 75—8 to 75—9 SGGLSE driver routine 75—7 SGGSVD, driver routine 75—22 to 75—23 Shader, Bryan L. 30—1 to 30—10 Shannon capacity 28—9 Shannon’s Coding theorem 61—3 to 61—4 Shape, matrices 1—3 Shapiro, Helene 7—1 to 7—9 Sherman — Morrison 14—15 Shestakov, Ivan P. 69—1 to 69—25 Shift and invert spectral transformation mode, ARPACK 76—7 Shift, symmetric matrix eigenvalue techniques 42—2 Shifted matrices 42—2 Shifted QR iteration 42—3 Shifts, polynomial restarting 44—6 Shor’s factorization algorithm, Grover’s search algorithm 62—17 Shor’s factorization algorithm, quantum computation 62—6 62—17 Show, Mathematica software 73—5 SIGN P—6 Sign changes 21—9 Sign function 11—12 Sign nonsingularity, rank revealing decomposition 46—8 Sign nonsingularity, sign-pattern matrices 33—3 to 33—5 Sign pattern 30—4 Sign pattern class, complex sign and ray patterns 33—14 Sign pattern class, sign-pattern matrices 33—1 Sign potentiallyorthogonality(SPO) 33—16 Sign semistability 33—7 Sign singularity, rank revealing decomposition 46—8 Sign singularity, sign nonsingularity 33—3 Sign solvability 33—5 to 33—7 Sign stable 33—7 Sign symmetric 19—3 Sign-central patterns 33—17 Sign-pattern matrices, allowing properties 33—9 to 33—11 Sign-pattern matrices, complex sign patterns 33—14 to 33—15 Sign-pattern matrices, eigenvalue characterizations 33—9 to 33—11 Sign-pattern matrices, fundamentals 33—1 to 33—3 Sign-pattern matrices, inertia, minimum rank 33—11 to 33—12 Sign-pattern matrices, inverses 33—12 to 33—14 Sign-pattern matrices, L-matrices 33—5 to 33—7 Sign-pattern matrices, orthogonality 33—16 to 33—17 Sign-pattern matrices, powers 33—15 to 33—16 Sign-pattern matrices, ray patterns 33—14 to 33—16 Sign-pattern matrices, S-matrices 33—5 to 33—7 Sign-pattern matrices, sign nonsingularity 33—3 to 33—5 Sign-pattern matrices, sign solvability 33—5 to 33—7 Sign-pattern matrices, sign-central patterns 33—17 Sign-pattern matrices, stability 33—7 to 33—9 Signal model 64—16 Signal processing, adaptive filtering 64—12 to 64—13 Signal processing, arrival estimation direction 64—15 to 64—18 Signal processing, fundamentals 64—1 to 64—4 Signal processing, linear prediction 64—7 to 64—9 Signal processing, random signals 64—4 to 64—7 Signal processing, spectral estimation 64—14 to 64—15 Signal processing, Wiener filtering 64—10 to 64—11 Signal subspace 64—16 Signature matrix, square case 32—2 Signature pattern 33—2 Signature similarity 33—2 Signature, Hermitian forms 12—8 Signature, symmetric bilinear forms 12—3 Signed 4-cockade 30—4 Signed bigraph 30—4 Signed bipartite graph 30—1 Signed digraphs 33—2 Signed singular value decomposition 46—16 Significand 37—11 Signing 33—5 Signless Laplacian matrix 28—7 Similarity of matrix families, classification I 24—7 to 24—10 Similarity of matrix families, classification II 24—10 to 24—11 Similarity of matrix families, fundamentals 24—1 to 24—5 Similarity of matrix families, property L 24—6 to 24—7 Similarity of matrix families, simultaneous similarity 24—5 to 24—11 Similarity, change of basis 3—4 Similarity, linear independence, span, and bases 2—7 Similarity, matrix similarities 24—1 Similarity-scaling 9—20 Simon’s problem 62—13 to 62—15 Simple algebras, general properties 69—4 Simple algebras, Lie algebras 70—3 to 70—7 Simple cycles, matrix completion problems 35—2 Simple cycles, sign-pattern matrices 33—2 simple eigenvalues 4—6
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