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Hogben L. — Handbook of Linear Algebra
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Название: Handbook of Linear AlgebraАвтор: Hogben L. Аннотация: 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.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2006Количество страниц: 1400Добавлена в каталог: 30.06.2008Операции: Положить на полку |
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probability 52—2 Probability and statistics applications, linear statistical models 52—1 to 52—15 Probability and statistics applications, Markov chains 54—1 to 54—14 Probability and statistics applications, multivariate statistical analysis 53—1 to 53—14 Probability and statistics applications, random vectors 52—1 to 52—15 Probability density function 52—2 Probability function 52—2 Probability vector 4—10 Procrustes problem 60—4 to 60—7 Product form 9—23 Product, algebraic connectivity 36—1 Product, characters 68—5 Product, vector spaces 3—2 Product-moment correlation 52—3 Profile methods 40—10 40—16 Profiles, reordering effect 40—14 Programming, associated linear programming 50—14 Programming, Delsarte’s Linear Programming Bound 28—12 Programming, dynamic 25—3 Programming, linear semidefinite 51—3 Programming, linear, canonical forms 50—7 to 50—8 Programming, linear, duality 50—13 to 50—17 Programming, linear, formulation 50—3 to 50—7 Programming, linear, fundamentals 50—1 to 50—2 Programming, linear, geometric interpretation, phase 2 50—13 Programming, linear, interior point methods 50—23 to 50—24 Programming, linear, linear approximation 50—20 to 50—23 Programming, linear, Mathematica software 73—23 to 73—24 Programming, linear, matrix games 50—18 to 50—20 Programming, linear, parametric programming 50—17 to 50—18 Programming, linear, phase 2 geometric interpretation 50—13 Programming, linear, pivoting 50—10 to 50—11 Programming, linear, sensitivity analysis 50—17 to 50—18 Programming, linear, simplex method 50—11 to 50—13 Programming, linear, standard forms 50—7 to 50—8 Programming, linear, standard row tableaux 50—8 to 50—10 Programming, LinearProgramming, Mathematica software 73—24 Programming, mathematical 50—1 Programming, Matlab software 71—11 to 71—14 Programming, parametric 50—17 to 50—18 Programming, programming, Matlab software 71—11 to 71—14 Programming, semidefinite (SDP), applications 51—9 to 51—11 Programming, semidefinite (SDP), constraint qualification 51—7 Programming, semidefinite (SDP), duality 51—5 to 51—7 Programming, semidefinite (SDP), fundamentals 51—1 to 51—3 Programming, semidefinite (SDP), geometry 51—5 Programming, semidefinite (SDP), notation 51—3 to 51—5 Programming, semidefinite (SDP), optimality conditions 51—5 to 51—7 Programming, semidefinite (SDP), primal-dual interior point algorithm 51—8 to 51—9 Programming, semidefinite (SDP), results 51—3 to 51—5 Programming, semidefinite (SDP), strong duality 51—7 Programming, symmetric cone 51—2 Projection formulas 44—2 Projection, Mathematica software 73—4 73—5 Projectionally exposed face 51—5 Projections 3—6 3—6 Projective general linear group 67—3 Projective plane, linear code classes 61—10 Projective plane, projective spaces 65—6 Projective spaces 65—6 to 65—9 Projective special linear group 67—3 Projective transformation 65—7 Propagator 59—10 Proper cones 26—1 Proper digraphs 29—2 Proper point, Euclidean simplexes 66—8 Properly signed nest 33—7 Properties, nonassociative algebra 69—4 to 69—8 Properties, numerical range 18—1 to 18—3 Property C, satisfying 9—17 Property L, similarity ofmatrixfamilies 24—6 to 24—7 Property L, spectral theory 7—5 Protein motion mode calculation 60—9 to 60—10 Proximity measure 53—13 PSD see «Positive definite matrices (PSD)» Pseudo-code 37—16 Pseudo-inverse 5—12 to 5—14 Pseudoeigenvalues 16—1 Pseudoeigenvectors 16—1 PseudoInverse, Mathematica software, linear systems 73—20 73—23 PseudoInverse, Mathematica software, matrix algebra 73—10 73—11 Pseudospectra, computation 16—11 to 16—12 Pseudospectra, extensions 16—12 to 16—15 Pseudospectra, fundamentals 16—1 to 16—5 Pseudospectra, matrix function behaviors 16—8 to 16—11 Pseudospectra, Toeplitz matrices 16—5 to 16—8 Pseudospectral abscissa, matrix function behavior 16—8 Pseudospectral radius 16—8 Pseudospectrum, convergence in gap 44—10 Pseudospectrum, rectangular matrix 16—12 Puiseaux expansion, matrix similarities 24—1 Puiseaux expansion, matrix similarity 24—2 Puiseux expansions 9—10 Puntanen, Simo 52—1 to 52—15 53—1 Pure strategies, matrix games 50—18 Q-norm 17—6 QFT (Quantum Fourier transform) 62—6 QMR (quasi-minimal residual) algorithm, Krylov space QMR (quasi-minimal residual) algorithm, methods 41—8 41—10 QMR (quasi-minimal residual) algorithm, linear systems of equations 49—13 QMR (quasi-minimal residual) algorithm, preconditioners 41—12 QR decomposition 38—13 to 38—15 QR factorization see «Factorizations» QR factorization, algorithm efficiency 37—17 QR factorization, Gram — Schmidt orthogonalization 5—8 to 5—10 QR factorization, least squares solutions 39—8 to 39—9 QR factorization, numerical stability and instability 37—20 QR factorization, orthogonal factorizations 39—5 QR factorization, preconditioned Jacobi SVD algorithm 46—5 QR factorization, rank revealing decomposition 39—11 QR iteration, explicit 43—5 to 43—6 QR iteration, symmetric matrix eigenvalue techniques 42—3 QR method see «Implicitly shifted QR method» QRDecomposition, Maple software 72—9 QRDecomposition, Mathematica software 73—18 Quadrangular bipartite graph 30—1 Quadratic algebras 69—8 Quadratic forms, fundamentals 12—1 12—3 Quadratic forms, matrices 53—8 to 53—11 Qualitative class, complex sign and ray patterns 33—14 Qualitative class, sign-pattern matrices 33—1 Quantum bit 62—2 Quantum circuit 62—2 Quantum computation, Bernstein — Vazirani problem 62—11 to 62—13 Quantum computation, Deutsch — Jozsa problem 62—9 to 62—11 Quantum computation, Deutsch’s problem 62—8 to 62—9 Quantum computation, fundamentals 62—1 to 62—7 Quantum computation, Grover’s search algorithm 62—15 to 62—17 Quantum computation, Shor’s factorization algorithm 62—17 to 62—19 Quantum computation, Simon’s problem 62—13 to 62—15 Quantum computation, universal quantum gates 62—7 to 62—8 Quantum Fourier transform (QFT) 62—6 Quantum register 62—2 Quantum Turing machine 62—2 Quarternions, generalized 69—4 Quartics, Mathematica software 73—14 Quasi-associative algebras 69—15 Quasi-irreducibility characteristics 24—8 24—11 Quasi-minimal residual (QMR) algorithm, Krylov space Quasi-minimal residual (QMR) algorithm, methods 41—8 Quasi-minimal residual (QMR) algorithm, linear systems ofequations 49—13 Quasi-minimal residual (QMR) algorithm, preconditioners 41—12 Quasi-triangular characteristics 43—6 Query module 63—9 Query processing 63—2 Query vector 63—2 Queueing system 54—4 Quotient algebra 69—4 Quotient field 23—1 Quotient representation 68—1 Quotient, direct sum decompositions 2—5 Radical algebras 69—5 70—4 RADIUS 18—6 to 18—8 Radix2 FFT 58—17 to 58—19 Raising operator 59—8 59—9 rand command, Matlab software 71—6 Random linear dynamical systems see «Dynamical systems» Random linear dynamical systems, fundamentals 56—14 to 56—16 Random linear dynamical systems, linear skew product flows 56—12 Random samples, data matrix 53—3 Random signals 64—4 to 64—7 Random vectors, fundamentals 52—1 to 52—8 Random vectors, linear statistical models 52—8 to 52—15 Random walk, Markov chains 54—3 to 54—4 Range, kernel 3—5 to 3—6 Range, least squares solution 39—4 Range, linear independence, span, and bases 2—6 Range, linear inequalities and projections 25—10 Range, Mathematica software 73—3 73—4 rank command, Matlab software 71—17 Rank Equalities method 2—7 to 2—8 Rank Inequalities method 2—7 to 2—8 Rank revealing 46—5 Rank revealing decomposition (RRD), high relative accuracy 46—7 to 46—10 Rank revealing decomposition (RRD), least squares solutions 39—11 to 39—12 Rank revealing QR (RRQR) decomposition 39—11 Rank, bilinear forms 12—2 Rank, combinatorial matrix theory 27—2 Rank, convolutional codes 61—11 Rank, decomposable tensors 13—7 Rank, decompositions, bipartite graphs 30—8 Rank, dimension theorem 2—6 to 2—9 Rank, Gaussian and Gauss-Jordan elimination 1—7 Rank, inertia 33—11 Rank, kernel and range 3—5 Rank, linear independence 2—6 25—13 Rank, Maple software 72—9 Rank, matrix equalities and inequalities 14—12 to 14—15 Rank, matrix range 2—6 to 2—9 Rank, null space 2—6 to 2—9 Rank, semisimple and simple algebras 70—4 Rank, sesquilinear forms 12—6 Rank-deficient least squares problem 5—14 Ranking module 63—9 Rate, linear block codes 61—3 Rational canonical forms (RCF), elementary divisors 6—8 to 6—11 Rational canonical forms (RCF), invariant forms 6—12 to 6—14 Rational canonical forms (RCF), matrix similarity 24—3 24—4 Rational similarity 24—1 Ravindrudu, Rahul 60—13 Ray nonsingular pattern 33—14 Ray patterns 33—14 to 33—16 Rayleigh quotient, Arnoldi factorization 44—3 Rayleigh quotient, Hermitian matrices 8—3 Rayleigh quotient, symmetric matrix eigenvalue techniques 42—3 Rayleigh quotient, total least squares problem 48—9 Rayleigh — Ritz inequalities 14—4 Rayleigh — Ritz theorem 8—3 8—4 8—5 RCF see «Rational canonical forms (RCF)» Reaction equations 60—10 Real affine space 65—2 Real division algebra 69—4 Real square matrices 19—5 19—9 Real structured pseudo-spectrum 16—12 Real — Jordan block 6—7 Real — Jordan canonical form 6—6 to 6—8 see Real — Jordan form 56—2 Real — Jordan matrix 6—7 Realization 57—6 Reams, Robert 10—1 to 10—9 Recall, vector space method 63—2 Recognition, matrix power asymptotics 25—8 Recognition, total positive and total negative matrices 21—6 to 21—7 Reconstructibility 57—2 Rectangular matrix multiplication 47—5 Rectangular matrix pseudo-spectrum 16—12 Recurrent state 54—7 to 54—9 Recursive least squares (RLS) 64—12 Reduce, Mathematica software 73—20 73—21 Reduced digraphs, irreducible matrices 29—7 Reduced digraphs, nonnegative and stochastic matrices 9—2 Reduced digraphs, reducible matrices 9—7 Reduced QR factorization 5—8 Reduced row echelon form (RREF), computational methods 69—23 69—25 Reduced row echelon form (RREF), Gaussian and Gauss-Jordan elimination 1—7 to 1—9 Reduced row echelon form (RREF), rank 2—6 Reduced row echelon form (RREF), systems of linear equations 1—10 to 1—11 1—12 1—13 Reduced singular value decomposition (reduced SVD), fundamentals 45—1 Reduced singular value decomposition (reduced SVD), singular value decomposition 5—10 to 5—11 Reduced-order model 49—14 ReducedRowEchelonForm, Maple software 72—9 72—10 Reducibility, group representations 68—1 Reducibility, matrix group 67—1 Reducibility, matrix representations 68—3 Reducibility, modules 70—7 Reducibility, square matrices, weak combinatorial invariants 27—5 Reducible matrices, cone invariant departure, matrices 26—8 to 26—10 Reducible matrices, fundamentals 9—7 to 9—15 Reducible matrices, max-plus eigenproblem 25—7 Reducible matrices, nonnegative matrices 9—7 to 9—15 Reducing eigenvalue 18—3 Redundancy 50—4 Reed-Solomon code 61—8 61—9 61—10 Ref see «Row echelon form (REF)» Reflection 70—4 Reflection coefficients 64—8 Reflection matrix 65—5 Regression, random vectors 52—4 Regressor vectors 52—8 Regular bimodule algebras 69—6 Regular graphs 28—3 Regular matrices 32—5 to 32—7 see Regular matrix pencils 55—7 Regular pencils 43—2 Regular point 24—8 Regular signals 64—7 Regular splitting, Krylov subspaces and preconditioners 41—3 Regular splitting, numerical methods 54—12 Regularly cyclic simplexes 66—12 Regulated output 57—14 Reinsch, Parlett and, studies 43—3 Relational functions field 23—2 Relational operators, Matlab software 71—12 Relative backward errors, linear system 38—2 Relative condition number 37—7 Relative distances 15—13 Relative errors, conditioning and condition numbers 37—7 Relative errors, floating point numbers 37—13 37—16 Relative perturbation theory, eigenvalue problems 15—13 to 15—15 Relative perturbation theory, singular value problems 15—15 to 15—16 Relative separation measure 17—7 Relevance, vector space method 63—2 Reordering effect 40—14 to 40—18 Representation, group representations 68—2 to 68—3 Representation, Malcev algebras 69—16 Representation, modules 70—7 Residual matrix 52—9 Residual sum of squares 52—8 Residual vector, least squares solution 39—1 Residual vector, linear system perturbations 38—2 Residuals, Krylov subspaces and preconditioners 41—2 Residuals, least squares problems 5—14 Residuals, linear approximation 50—20 Residuals, linear statistical models 52—8 Residuals, random vectors 52—4 Resistive electrical networks 66—13 to 66—15 Resolvents, expansions 9—10 Resolvents, nonnegatives 26—13 Resolvents, pseudospectra 16—1 Respectively definite matrices 51—3 Rest, Mathematica software 73—3 73—13 Restarted GMRES algorithm 41—7
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