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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
Linear algebra, isomorphism 3—7 to 3—8 Linear algebra, kernel 3—5 to 3—6 Linear algebra, least-squares problems 5—14 to 5—16 Linear algebra, linear functionals 3—8 to 3—9 Linear algebra, linear independence 2—1 to 2—3 Linear algebra, linear transformations 3—1 to 3—9 Linear algebra, LU factorization 1—13 to 1—15 Linear algebra, Maple software 72—12 to 72—13 Linear algebra, matrices 1—3 to 1—6 1—11 2—6 3—3 Linear algebra, nilpotence 2—12 Linear algebra, nonsingularity characterizations 2—9 to 2—10 3—7 Linear algebra, null space 2—6 to 2—9 Linear algebra, orthogonal projection 5—6 to 5—8 Linear algebra, orthogonality 5—3 to 5—10 Linear algebra, projections 3—6 to 3—7 Linear algebra, pseudo-inverse 5—12 to 5—14 Linear algebra, QR factorization 5—8 to 5—10 Linear algebra, range 3—5 to 3—6 Linear algebra, rank 2—6 to 2—9 Linear algebra, similarity 3—4 Linear algebra, singular value decomposition 5—10 to 5—12 Linear algebra, span 2—1 to 2—3 Linear algebra, systems of linear equations 1—9 to 1—11 Linear algebra, transformations, linear 3—1 to 3—9 Linear algebra, vectors 1—1 to 1—3 2—3 3—2 Linear block codes 61—3 to 61—4 Linear characters 68—5 Linear code classes 61—6 to 61—11 Linear combination, Euclidean point space 66—2 Linear combination, span and linear independence 2—1 Linear constraints 50—1 Linear dependence 2—1 66—2 Linear differential equation of order 55—1 Linear differential equations, differential equations 55—1 to 55—5 Linear differential equations, dynamical systems 56—2 to 56—4 Linear differential equations, numerical methods 54—12 Linear differential-algebraic equations 55—7 to 55—10 55—14 Linear dynamical systems 49—14 to 49—15 56—5 see «Linear Linear equality-constrained least squares problems 75—6 to 75—7 Linear equations, cone invariant departure, matrices 26—11 to 26—12 Linear equations, matrices over integral domains 23—8 to 23—9 Linear equations, systems of linear equations 1—9 Linear form, linear functionals and annihilator 3—8 Linear form, linear programming 50—1 Linear functionals, annihilator 3—8 to 3—9 Linear hull 66—2 Linear independence and rank, Euclidean point space 66—2 Linear independence and rank, max-plus algebra 25—12 to 25—14 Linear independence and rank, span 2—1 to 2—3 Linear inequalities and projections 25—10 to 25—12 Linear least squares problems 75—4 to 75—6 Linear maps 3—1 13—8 see Linear matrix groups 67—3 to 67—5 Linear matrix similarities 24—1 Linear model problem 75—8 to 75—9 Linear operators, linear transformations 3—1 Linear operators, nonassociative algebra 69—3 Linear ordinary differential equations, fundamentals 55—5 to 55—6 Linear ordinary differential equations, stability 55—10 to 55—14 Linear output feedback 57—7 Linear prediction 64—7 to 64—9 Linear preserver problems, additive preservers 22—7 to 22—8 Linear preserver problems, fundamentals 22—1 to 22—2 Linear preserver problems, multiplicative preservers 22—7 to 22—8 Linear preserver problems, nonlinear preservers 22—7 to 22—8 Linear preserver problems, problems 22—4 to 22—7 Linear preserver problems, standard forms 22—2 to 22—4 Linear programming, canonical forms 50—7 to 50—8 Linear programming, duality 50—13 to 50—17 Linear programming, formulation 50—3 to 50—7 Linear programming, fundamentals 50—1 to 50—2 Linear programming, geometric interpretation, phase 2 50—13 Linear programming, interior point methods 50—23 to 50—24 Linear programming, linear approximation 50—20 to 50—23 Linear programming, Mathematica software 73—23 to 73—24 Linear programming, matrix games 50—18 to 50—20 Linear programming, parametric programming 50—17 to 50—18 Linear programming, phase 2 geometric interpretation 50—13 Linear programming, pivoting 50—10 to 50—11 Linear programming, sensitivity analysis 50—17 to 50—18 Linear programming, simplex method 50—11 to 50—13 Linear programming, standard forms 50—7 to 50—8 Linear programming, standard row tableaux 50—8 to 50—10 Linear programs 50—2 Linear representation 68—1 Linear semidefinite programming 51—3 Linear skew product flows 56—11 to 56—12 Linear state feedback 57—7 Linear statistical models, fundamentals 52—8 to 52—15 Linear statistical models, random vectors 52—1 to 52—8 Linear subspaces 66—2 Linear system perturbations 38—2 to 38—5 Linear systems ofequations, LAPACK subroutine package 75—2 to 75—4 Linear systems ofequations, large-scale matrix computations 49—12 to 49—15 Linear systems, conditioning, error analysis 37—9 to 37—11 Linear systems, direct solution, fundamentals 38—1 Linear systems, direct solution, Gauss elimination 38—7 to 38—12 Linear systems, direct solution, LU decomposition 38—7 to 38—12 Linear systems, direct solution, orthogonalization 38—13 to 38—15 Linear systems, direct solution, perturbations 38—2 to 38—5 Linear systems, direct solution, QR decomposition 38—13 to 38—15 Linear systems, direct solution, symmetric factorizations 38—15 to 38—17 Linear systems, direct solution, triangular linear systems 38—5 to 38—7 Linear systems, dynamical 49—14 to 49—15 Linear systems, equations 49—12 to 49—15 Linear systems, fundamentals 1—9 Linear systems, iterative solution methods, CG convergence Linear systems, iterative solution methods, rates 41—14 to 41—15 Linear systems, iterative solution methods, convergence rates 41—14 to 41—16 Linear systems, iterative solution methods, error estimation 41—16 to 41—17 Linear systems, iterative solution methods, finite precision arithmetic 41—16 to 41—17 Linear systems, iterative solution methods, fundamentals 41—1 to 41—2 Linear systems, iterative solution methods, GMRES convergence rates 41—15 to 41—16 Linear systems, iterative solution methods, Hermitian problems 41—4 to 41—7 Linear systems, iterative solution methods, inexact preconditioners 41—16 to 41—17 Linear systems, iterative solution methods, Krylov subspaces 41—2 to 41—4 Linear systems, iterative solution methods, MINRES convergence rates 41—14 to 41—15 Linear systems, iterative solution methods, non-Hermitian problems 41—7 to 41—11 Linear systems, iterative solution methods, non-optimal Krylov space methods 41—7 to 41—11 Linear systems, iterative solution methods, optimal Krylov space methods 41—4 to 41—11 Linear systems, iterative solution methods, preconditioned algorithms 41—12 to 41—14 Linear systems, iterative solution methods, preconditioners 41—2 to 41—4 41—11 Linear systems, iterative solution methods, stopping criteria 41—16 to 41—17 Linear systems, large-scale matrix computations 49—12 to 49—15 Linear systems, least squares solutions, algebraic aspects 39—4 to 39—5 Linear systems, least squares solutions, algorithms 39—6 to 39—7 Linear systems, least squares solutions, damped least squares 39—9 to 39—10 Linear systems, least squares solutions, data fitting 39—3 to 39—4 Linear systems, least squares solutions, downdating 39—8 to 39—9 Linear systems, least squares solutions, fundamentals 39—1 to 39—3 Linear systems, least squares solutions, geometric aspects 39—4 to 39—5 Linear systems, least squares solutions, orthogonal factorizations 39—5 to 39—6 Linear systems, least squares solutions, QR factorization 39—8 to 39—9 Linear systems, least squares solutions, rank revealing decompositions 39—11 to 39—12 Linear systems, least squares solutions, sensitivity 39—7 to 39—8 Linear systems, least squares solutions, updating 39—8 to 39—9 Linear systems, Mathematica software 73—20 to 73—23 Linear systems, Matlab software 71—7 to 71—9 Linear systems, structured matrices computations 48—5 to 48—8 Linear time-invariant (LTI) systems, analysis 57—7 to 57—10 Linear time-invariant (LTI) systems, control theory 57—2 Linear time-invariant (LTI) systems, signal processing 64—1 Linear transformations, Euclidean spaces 65—4 Linear transformations, linear algebra 3—1 to 3—9 Linear unbiased estimator 52—9 Linear zero function 52—9 Linear-quadratic Gaussian (LQG) problem 57—14 Linear-quadratic regulator (LQR) problem 57—14 LinearAlgebra package, Maple 72—1 72—2 LinearAlgebra[Modular], Maple software 72—12 to 72—13 LinearAlgebra’Cholesky’, Mathematica software 73—27 LinearAlgebra’MatrixManipulation’ package, Mathematica software 73—2 LinearAlgebra’MatrixManipulation’, Mathematica software, decomposition 73—19 LinearAlgebra’MatrixManipulation’, Mathematica software, fundamentals 73—26 LinearAlgebra’MatrixManipulation’, Mathematica software, linear systems 73—22 LinearAlgebra’Orthogonalization’ package, Mathematica software 73—4 73—5 LinearAlgebra’Tridiagonal’, Mathematica software 73—20 LinearEquationsToMatrices, Mathematica 73—20 73—22 Linearization, alternative algebras 69—11 Linearization, dynamical systems 56—19 to 56—21 Linearization, Jordan algebras 69—12 LinearProgramming, Mathematica software 73—24 LinearSolve, Maple software 72—9 LinearSolve, Mathematica software, decomposition 73—19 LinearSolve, Mathematica software, linear systems 73—20 73—21 73—22 Lines, affine spaces 65—2 Lines, Euclidean point space 66—2 Lines, matrices 27—2 Lines, projective spaces 65—6 lines, segments 50—13 65—2 Linklesly embedded graphs 28—4 ListDensityPlot, Mathematica software 73—27 Local invariant polynomials 23—9 Local Perron — Schaefer conditions 26—6 Local similarity 22—7 24—1 Local spectral radius 26—2 Local stable/unstable manifold 56—19 Location, numerical range 18—4 to 18—6 Loewner ordering 8—10 Loewner partial ordering 52—4 Loewy, Raphael 12—1 to 12—9 Log, Mathematica software 73—26 Log-barrier problem 51—8 Logarithms 11—6 Logical operators, Matlab software 71—12 Look-ahead strategies 40—17 41—10 Loop digraphs 29—2 Loop graphs 28—1 Lorentz cone 51—2 Lovasz parameter 28—10 Low density parity check (LDPC) codes 61—11 Lower bounds 47—8 Lower Collatz — Wielandt numbers 26—4 Lower Hessenberg matrices 10—4 Lower shift matrices 48—1 Lower triangular linear matrix 38—5 Lower triangular matrices 1—4 10—4 LowerDiagonalMatrix, Mathematica software 73—6 Lowering operator 59—8 59—9 Lowner partial ordering 52—4 LQG (linear-quadratic Gaussian) problem 57—14 LQR (linear-quadratic regulator) problem 57—14 LSI see «Latent semantic indexing (LSI)» LTI (linear time-invariant) systems, analysis 57—7 to 57—10 LTI (linear time-invariant) systems, control theory 57—2 57—7 LTI (linear time-invariant) systems, signal processing 64—1 LU decomposition, direct solution of linear systems 38—7 to 38—12 LU decomposition, incomplete LU decomposition 41—11 LU factorizations, Gaussian Eliminations 1—13 to 1—15 LU factorizations, sparse matrix factorizations 49—3 LUBackSubstitute, Mathematica software 73—19 LUBackSubstitution, Mathematica software 73—20 73—22 LUDecomposition, Maple software 72—9 72—10 LUDecomposition, Mathematica software, decomposition 73—18 73—19 LUDecomposition, Mathematica software, linear systems 73—20 73—22 Luenberger observer 57—11 57—12 57—13 LUMatrices, Mathematica software 73—19 Lyapunov equation, differential equations 55—11 Lyapunov equation, differential-algebraic equations 55—15 to 55—16 Lyapunov equation, matrix equations 57—10 Lyapunov equation, semidefinite programming 51—9 Lyapunov exponents, Floquet theory 56—13 Lyapunov exponents, linear differential equations 56—2 Lyapunov exponents, linear skew product flows 56—11 Lyapunov exponents, linearization 56—21 Lyapunov exponents, random linear dynamical systems 56—15 56—16 Lyapunov properties, diagonal stability 19—9 to 19—10 Lyapunov properties, scaling factor 19—9 Lyapunov properties, spectrum 56—16 56—17 Lyapunov properties, stability 55—10 55—14 Lyapunov spaces, Grassmannian and flag manifolds 56—10 56—11 Lyapunov spaces, linear differential equations 56—2 Lyapunov spaces, random linear dynamical systems 56—15 Lyapunov Stability Criterion 19—4 M- and 35—12 to 35—13 M-files, Matlab software 71—11 71—20 M-matrices, fundamentals 9—17 to 9—20 M-matrices, matrix completion problems 35—12 to 35—13 M-matrices, stability 19—4 M-norm 37—2 Machado, Armando 13—1 to 13—26 Machine epsilon 37—12 Mackey’s Subgroup theorem 68—9 Main angles, adjacency matrix 28—5 Main Coding Theory Problem 61—5 Main diagonal, matrices 1—4 Main Linear Coding Problem 61—5 to 61—6 61—12 Majorization P—4 Malcev algebras 69—2 69—3 69—16 Malcev module 69—16 Malcev theorem 67—2 Manipulation of matrices 73—13 to 73—14 Mantissa 37—11 Map, Mathematica software, decomposition 73—19 Map, Mathematica software, eigenvalues 73—16 Map, Mathematica software, fundamentals 73—26 Map, Mathematica software, matrices 73—7 Map, Mathematica software, matrix algebra 73—10 Map, Mathematica software, singular values 73—17 Maple software, arrays 72—8 to 72—9 Maple software, canonical forms 72—15 to 72—16 Maple software, eigenvalues and eigenvectors 72—11 to 72—12 Maple software, equation solving 72—9 to 72—11 Maple software, functions of matrices 72—19 to 72—20 Maple software, fundamentals 72—1 to 72—2 Maple software, linear algebra 72—12 to 72—13 Maple software, matrices 72—4 to 72—7 Maple software, matrix factoring 72—9 to 72—11 Maple software, modular arithmetic 72—12 to 72—13 Maple software, numerical linear algebra 72—13 to 72—15 Maple software, stability of matrices 72—20 to 72—21 Maple software, structured matrices 72—16 to 72—18 Maple software, vectors 72—2 to 72—4 Mapping theorems 16—2 MapThread, Mathematica software 73—13 Markov chains, censoring 54—11 Markov chains, doubly stochastic matrices 27—10 Markov chains, eigenvalues and eigenvectors 4—10 Markov chains, finite 54—9 to 54—11 Markov chains, fundamentals 54—1 to 54—5 Markov chains, irreducible classes 54—5 to 54—7 Markov chains, numerical methods 54—12 to 54—14 Markov chains, Perron — Schaefer condition 26—7 Markov chains, states classification 54—7 to 54—9 Markov decision process, deterministic 25—3 Markowitz cost 40—17 Markowitz scheme 40—18 Maschke’s theorem, group representations 68—2 Maschke’s theorem, matrix groups 67—2 Maschke’s theorem, matrix representations 68—4 Matching, bipartite graphs 30—2 Mathematica software, appendix 73—25 to 73—27 Mathematica software, decompositions 73—18 to 73—19 Mathematica software, eigenvalues 73—14 to 73—16 Mathematica software, fundamentals 73—1 to 73—2 73—25 Mathematica software, linear programming 73—23 to 73—24 Mathematica software, linear systems 73—20 to 73—23 Mathematica software, manipulation of matrices 73—13 to 73—14 Mathematica software, matrices 73—5 to 73—9 Mathematica software, matrix algebra 73—9 to 73—12 Mathematica software, singular values 73—16 to 73—18
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