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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 |
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Ïðåäìåòíûé óêàçàòåëü
Strong Arnold Hypothesis 28—9 28—10 Strong combinatorial invariants 27—1 27—3 Strong connections 9—2 Strong duality, duality and optimality conditions 51—6 Strong duality, semidefinite programming 51—7 Strong nonsingularity 47—9 Strong Parter vertex 34—2 Strong preservation 22—1 Strong product 28—2 Strong rank 25—13 Strong sign nonsingularity 33—3 Strong stability 37—18 Strongly connected components, irreducible matrices 29—7 Strongly connected components, Jordan algebras 69—13 Strongly connected digraphs 29—6 to 29—8 Strongly inertia preserving 19—9 Strongly regular graphs 28—3 Strongly stable matrices 19—7 Structure and invariants 27—1 to 27—3 Structure constants 69—2 Structure index 63—9 Structure matrix 27—7 Structured matrices, computations, direct Toeplitz solvers 48—4 to 48—5 Structured matrices, computations, fundamentals 48—1 to 48—4 Structured matrices, computations, iterative Toeplitz solvers 48—5 Structured matrices, computations, linear systems 48—5 to 48—8 Structured matrices, computations, total least squares problems 48—8 to 48—9 Structured matrices, high relative accuracy 46—7 to 46—10 Structured matrices, Maple software 72—16 to 72—18 Structured pseudospectrum 16—12 Stuart, Jeffrey L. 6—14 29—1 Studham, Matthew 60—13 Sturn-Liouville problem 20—10 Styan, Evelyn Mathason 53—14 Styan, George P.H. 52—1 to 52—15 53—1 Stykel, Tatjana 55—1 to 55—16 Sub-bimodules 69—6 Subalgebra 69—3 Subdigraphs 29—2 Subgraph 28—2 Submatrices, fundamentals 1—4 1—6 Submatrices, Gaussian and Gauss — Jordan elimination 1—8 to 1—9 Submatrices, inequalities 17—7 Submatrices, Matlab software 71—1 to 71—3 Submatrices, partitioned matrices 10—1 to 10—3 SubMatrix, Mathematica software 73—13 Submodules, Bezout domains 23—8 Submodules, modules 70—7 Submultiplicative properties 18—6 Subnormal floating point numbers 37—11 Suboptimal control problem 57—15 Subordinate matrix norms 37—4 Subpatterns, sign-pattern matrices 33—2 Subpermanents 31—9 to 31—10 Subrepresentation 68—1 Subroutine packages, ARPACK 76—1 to 76—10 Subroutine packages, BLAS 74—1 to 74—7 Subroutine packages, EIGS 76—1 to 76—10 Subroutine packages, LAPACK 75—1 to 75—23 subs command, Matlab software 71—17 71—18 Subsemimodules 25—2 Subspaces, direct sum decompositions 2—5 Subspaces, direction, arrival estimation 64—16 Subspaces, implicitly restarted Arnoldi method 44—9 to 44—10 Subspaces, iteration 42—2 Subspaces, nonassociative algebra 69—3 Subspaces, vector spaces 1—2 Substochastic matrices 9—15 to 9—17 Subtractive cancellation, conditioning and condition numbers 37—8 Subtractive cancellation, floating point numbers 37—15 Subtractive cancellation, significant digits 37—13 Subtuple theorem 20—7 Successive overrelaxation (SOR) methods 41—3 to 41—4 Sufficient conditions 20—8 to 20—10 sum command, Matlab software 71—17 Sum of squares, residual 52—8 Sum, characters 68—5 Sum, direct sum decompositions 2—5 Sum, vector spaces 3—2 Sum-norm 37—2 Sun lemma, eigenvalue problems 15—10 Sun lemma, singular value problems 15—12 Sup-norm 37—2 Superposition Principle, double generalized stars 34—12 to 34—14 Superposition Principle, mathematical physics 59—1 Superposition Principle, quantum computation 62—1 to 62—2 supply, Mathematica software 73—24 Support line 18—3 Support, linear inequalities and projections 25—10 Support, scaling nonnegative matrices 9—21 Support, square matrices, strong combinatorial invariants 27—3 surfc command, Matlab software 71—15 Surjective, kernel and range 3—5 Surplus variables 50—7 Suttle’s algebra 69—15 Suttle’s example 69—8 SVD see «Singular value decomposition (SVD)» Sweedler notation 69—20 Sweep, Jacobi method 42—18 Switch, Mathematica software 73—8 Switching equivalent 28—8 Sylvester’s equation 57—10 57—11 Sylvester’s Identity 4—5 Sylvester’s law of nullity 14—13 Sylvester’s laws of inertia, congruence 8—6 Sylvester’s laws of inertia, Hermitian forms 12—8 to 12—9 Sylvester’s laws of inertia, symmetric bilinear forms 12—4 Sylvester’s observer equation 57—12 Sylvester’s theorem 42—14 sym command, Matlab software 71—17 Sym multiplication 13—17 to 13—19 Symbol curve, Toeplitz matrices 16—6 Symbolic mathematics 71—17 to 71—19 Symbols, Toeplitz matrices 16—6 Symmetric algebra, Lie algebras 70—2 Symmetric algebra, tensor algebras 13—22 Symmetric matrices see «Multiplicity lists» Symmetric matrices, direct sum decompositions 2—5 Symmetric matrices, fundamentals 1—6 Symmetric matrices, invariance 3—7 Symmetric matrices, kernel and range 3—6 Symmetric matrices, Maple software 72—14 Symmetric matrices, semidefinite programming 51—3 Symmetric matrix eigenvalue techniques, bisection method 42—14 to 42—15 Symmetric matrix eigenvalue techniques, comparison ofmethods 42—21 to 42—22 Symmetric matrix eigenvalue techniques, divide and conquer method 42—12 to 42—14 Symmetric matrix eigenvalue techniques, fundamentals 42—1 to 42—2 Symmetric matrix eigenvalue techniques, implicitly shifted QR method 42—9 to 42—11 Symmetric matrix eigenvalue techniques, inverse iteration 42—14 to 42—15 Symmetric matrix eigenvalue techniques, Jacobi method 42—17 to 42—19 Symmetric matrix eigenvalue techniques, Lanczos method 42—19 to 42—21 Symmetric matrix eigenvalue techniques, method comparison 42—21 to 42—22 Symmetric matrix eigenvalue techniques, methods 42—2 to 42—5 Symmetric matrix eigenvalue techniques, multiple relatively Symmetric matrix eigenvalue techniques, robust representations 42—15 to 42—17 Symmetric matrix eigenvalue techniques, tridiagonalization 42—5 to 42—9 Symmetric properties, asymmetric maps 13—10 to 13—12 Symmetric properties, bilinear forms 12—3 to 12—5 Symmetric properties, cone programming 51—2 Symmetric properties, definite eigenproblems 75—15 to 75—17 Symmetric properties, digraphs 35—2 Symmetric properties, dissimilarity 53—13 Symmetric properties, eigenvalue problems 75—9 to 75—11 Symmetric properties, factorizations 38—15 to 38—17 Symmetric properties, form 12—1 to 12—5 Symmetric properties, function, elementary P—2 to P—3 Symmetric properties, group representations 68—10 to 68—11 Symmetric properties, Hamiltonian, minimally chordal 35—15 Symmetric properties, Hermitian matrices 8—1 Symmetric properties, indefinite matrices 46—14 to 46—16 Symmetric properties, inertia set 33—11 Symmetric properties, Kronecker product 51—3 Symmetric properties, Lanczos process 49—6 to 49—7 Symmetric properties, maps 13—10 to 13—12 Symmetric properties, matrices 1—4 Symmetric properties, matrix games 50—18 Symmetric properties, maximal rank 33—11 Symmetric properties, minimal rank 33—11 Symmetric properties, positive definite matrices 40—11 Symmetric properties, product 13—13 Symmetric properties, reducible matrices 9—11 to 9—12 Symmetric properties, scaling 9—20 27—10 Symmetric properties, tensors 13—12 to 13—17 Symmetric rank revealing decomposition (SRRD) 46—14 Symmetrization 25—13 Symmetrized rank 25—13 Symplectic group 67—5 syms command, Matlab software 71—17 Syndrome of y 61—3 Systematic encoder 61—3 Systems analysis 58—7 Systems of linear equations 1—9 to 1—11 Table, Mathematica software, linear programming 73—24 Table, Mathematica software, matrices 73—6 73—8 Table, Mathematica software, singular values 73—18 Table, Mathematica software, vectors 73—3 73—4 Tablespacing, Mathematica software 73—7 Take, Mathematica software, matrices manipulation 73—13 Take, Mathematica software, vectors 73—3 TakeColumns, Mathematica software 73—13 TakeMatrix, Mathematica software 73—13 TakeRows, Mathematica software 73—13 Tam, Bit-Shun 26—1 to 26—14 Tam, T.Y. 68—1 to 68—11 Tam-Schneider condition 26—7 Tangent space 65—2 tangents 24—1 24—2 Tanner, M. 61—11 Tao, Knutson and, studies, eigenvalues 17—13 Tao, Knutson and, studies, Hermitian matrices 8—4 Taussky, Motzkin and, studies 7—8 Taylor coefficients 49—15 Taylor series 37—20 to 37—21 Taylor series expansion, irreducible matrices 9—5 Taylor series expansion, matrix function 11—3 to 11—4 Templates, ARPACK 76—8 Tensor algebras 13—20 to 13—22 70—2 Tensor products 10—8 68—3 Tensors, algebras 13—20 to 13—22 Tensors, decomposable tensors 13—7 Tensors, Grassmann tensors 13—12 to 13—17 Tensors, inner product spaces 13—22 to 13—24 Tensors, linear maps 13—8 to 13—10 Tensors, matrix similarities 24—1 Tensors, multiplication 13—17 to 13—19 Tensors, products 13—3 to 13—7 13—8 13—22 Tensors, symmetric tensors 13—12 to 13—17 Term rank, combinatorial matrix theory 27—2 Term rank, inertia 33—11 Term-by-document matrix 63—1 Term-wise singular value inequalities 17—9 Ternary Golay code 61—8 61—9 Testing 21—6 to 21—7 Text, Mathematica software 73—5 TFQMR (transpose-free quasi-minimal residual) linear systems ofequations 49—14 TGEVC LAPACK subroutine 43—7 TGSEN LAPACK subroutine 43—7 TGSNA LAPACK subroutine 43—7 th cofactor 4—1 th compound matrix 4—3 th minor 4—1 Thompson’s Standard Additive inequalities 17—8 Thompson’s Standard Multiplicative inequalities 17—8 Thread, Mathematica software, fundamentals 73—26 Thread, Mathematica software, linear programming 73—24 Thread, Mathematica software, linear systems 73—20 73—22 Threshold pivoting 38—10 Ties-to-even standard 37—12 Tight sign-central matrices 33—17 Tikhonov regularization 39—9 Time space 54—1 Time varying linear differential equations 56—11 Time-invariance 57—2 Time-map 56—5 Timed event graphs 25—4 Tisseur, Higham and, studies 16—12 Tits system 67—4 toeplitz function, Matlab software 71—6 Toeplitz IEPs (ToIEPs) 20—10 Toeplitz matrices, direct Toeplitz solvers 48—4 to 48—5 Toeplitz matrices, iterative Toeplitz solvers 48—5 Toeplitz matrices, least squares algorithms 39—7 Toeplitz matrices, linear prediction 64—8 Toeplitz matrices, Maple software 72—18 Toeplitz matrices, pseudospectra 16—5 to 16—8 Toeplitz matrices, structured matrices 48—1 48—4 Toeplitz matrices, totally positive and negative matrices 21—12 Toeplitz operator 16—5 Toeplitz-Block matrices 48—3 Toeplitz-like matrices 48—5 to 48—6 Toeplitz-plus-band matrices 48—5 48—7 Toeplitz-plus-Hankel matrices 48—5 48—6 ToIEPs (Toeplitz IEPs) 20—10 Tolerance, Mathematica software, matrix algebra 73—11 Tolerance, Mathematica software, singular values 73—17 Top-down algorithm 40—17 Topic drift 63—13 to 63—14 Topological conjugacy 56—5 Topological equivalence 56—5 Torus 70—4 Total degree 23—2 Total least squares problems 39—2 48—8 Total memory 61—12 Total positive and total negative matrices, deeper properties 21—9 to 21—12 Total positive and total negative matrices, factorizations 21—5 to 21—6 Total positive and total negative matrices, fundamentals 21—1 Total positive and total negative matrices, properties 21—2 to 21—4 Total positive and total negative matrices, recognition 21—6 to 21—7 Total positive and total negative matrices, spectral properties 21—8 Total positive and total negative matrices, testing 21—6 to 21—7 Total signed compound (TSC), rank revealing decomposition 46—8 Total signed compound (TSC), rank revealing decompositions 46—9 46—10 Total support 27—3 Total variance 53—5 Total, Mathematica software, fundamentals 73—27 Total, Mathematica software, linear programming 73—24 Total, Mathematica software, linear systems 73—23 Total, Mathematica software, matrices 73—7 73—9 Total, Mathematica software, vectors 73—3 73—5 Totally hyperacute simplexes 66—10 Totally nonnegative matrix 46—10 Totally positive matrices 21—12 Totally unimodular 46—8 Tournament matrices 27—8 to 27—10 Tr, Mathematica software 73—7 Trace 1—4 3—3 trace command, Matlab software 71—17 Trace debugging capability, ARPACK 76—7 Trace norm 17—6 Trace, composition algebras 69—8 Trace-minimal graph 32—9 Trace-sequence 32—9 Trailing diagonal 15—12 Trajectory see «Orbit» Transfer function, dimension reduction 49—14 Transfer function, frequency-domain analysis 57—5 Transfer function, signal processing 64—2 Transform principal component 26—12 Transform, ATLAST 71—22 Transformations, linear 3—1 to 3—9 Transience 9—8 9—11
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