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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
Euclidean norm, preconditioned Jacobi SVD algorithm 46—6 46—7 Euclidean norm, rank revealing decompositions 46—8 Euclidean norm, symmetric indefinite matrices 46—14 Euclidean norm, vector norms 37—2 Euclidean Parallel Postulate, Generalized 65—3 Euclidean properties, matrices 53—14 Euclidean properties, plane 65—4 Euclidean properties, point space 66—1 to 66—5 Euclidean properties, projective spaces 65—9 Euclidean properties, simplexes 66—7 to 66—10 Euclidean properties, unitary similarity 7—2 Euclidean spaces, Gram matrices 66—5 Euclidean spaces, inner product spaces 5—2 Euclidean spaces, orthogonality 5—5 Euclidean spaces, semisimple and simple algebras 70—4 Euclidean spaces, vector spaces 1—3 Euclid’s algorithm, certain integral domains 23—2 Euclid’s algorithm, matrix equivalence 23—7 Evaluation, permanents 31—11 to 31—12 EVD (eigenvalue decomposition) 42—2 Even cycle 33—2 Exact breakdown 49—8 Exact numerical cancellation 40—4 Exact shifts 44—6 Exactly universal quantum gates 62—7 Exceptional, Jordan algebra, Jordan algebras 69—12 Exceptional, Jordan algebra, nonassociative algebra 69—3 Exogenous input 57—14 exp command, Matlab software 71—19 Expand, Mathematica software 73—25 Expanders, graph parameters 28—9 Expansion, Bezout domains 23—9 Expansion, determinants 4—1 to 4—2 Expansion, reducible matrices 9—8 9—11 Expectation 52—2 52—3 Expected value, random vectors 52—3 Expected value, Schrodinger’s equation 59—7 Expected value, state estimation 57—12 Expected value, statistics and random variables 52—2 Explicit QR iteration 43—4 to 43—5 Explicit restarting 44—6 expm function, Matlab software 11—11 Exponent of matrix multiplication complexity 47—2 Exponential stability, linear differential equations 56—3 Exponential stability, linear differential-algebraic equations 55—14 Exponential stability, linear ordinary differential equations 55—10 Exponentials 56—2 Exponents, floating point numbers 37—11 Exponents, linear skew product flows 56—11 Exponents, primitive digraphs and matrices 29—9 expr, Mathematica software 73—26 Extended colored graphs 66—10 Extended graphs 66—10 Extended precision 37—13 Extended Tam — Schneider condition 26—7 Extendible characters 68—9 Extensions, pseudospectra 16—12 to 16—15 Extensions, sign solvability 33—5 Exterior algebra 70—2 Exterior point method 50—23 Exterior power 13—12 Exterior product 13—13 External direct sum, direct sum decompositions 2—5 External direct sum, nonassociative algebra 69—3 External product 13—25 Extremal generators 25—12 Extreme pathways 60—10 Extreme point 50—13 Extreme ray, flux balancing equation 60—10 Extreme ray, linear independence and rank 25—12 extreme values 27—7 Extreme vectors 26—2 ezcontour command, Matlab software 71—15 ezplot command, Matlab software 71—14 71—14 71—17 ezsurf command, Matlab software 71—17 F-distribution 53—10 F-ratio 53—3 Faber and Manteuffel theorem 41—8 Face, Collatz — Wielandt sets 26—5 Face, Euclidean simplexes 66—7 Face, geometry 51—5 Face, Perron — Frobenius theorem 26—2 Face, reducible matrices 26—8 Facially exposed face 51—5 Factorizations see «QR factorization» Factorizations, Arnoldi factorization 44—2 to 44—4 Factorizations, bipartite graphs 30—8 to 30—10 Factorizations, direct solution oflinear solutions, fundamentals 38—1 Factorizations, direct solution oflinear solutions, Gauss elimination 38—7 to 38—12 Factorizations, direct solution oflinear solutions, LU decomposition 38—7 to 38—12 Factorizations, direct solution oflinear solutions, orthogonalization 38—13 to 38—15 Factorizations, direct solution oflinear solutions, perturbations 38—2 to 38—5 Factorizations, direct solution oflinear solutions, QR decomposition 38—13 to 38—15 Factorizations, direct solution oflinear solutions, symmetric factorizations 38—15 to 38—17 Factorizations, direct solution oflinear solutions, triangular linear systems 38—5 to 38—7 Factorizations, function computation methods 11—9 to 11—10 Factorizations, information retrieval 63—5 to 63—8 Factorizations, LU factorizations 1—13 Factorizations, nonnegative matrix factorization 63—5 to 63—8 Factorizations, orthogonal, least squares solutions 39—5 to 39—6 Factorizations, sparse matrix methods 40—4 to 40—10 Factorizations, total positive and total negative matrices 21—5 to 21—6 Faithful characteristics, characters 68—5 Faithful characteristics, group representations 68—2 Faithful characteristics, matrix representations 68—3 Fallat, Shaun M. 21—1 to 21—12 Fast algorithms 47—2 to 47—4 see Fast Fourier transform (FFT) 58—17 to 58—20 60—8 Fast large-scale matrix computations 49—2 Fast matrix inversion 47—9 to 47—10 Fast matrix multiplication, advanced techniques 47—7 to 47—9 Fast matrix multiplication, algorithms 47—2 to 47—5 Fast matrix multiplication, applications 47—9 to 47—10 Fast matrix multiplication, approximation algorithms 47—6 to 47—7 Fast matrix multiplication, fundamentals 47—1 to 47—2 Feasible region 50—1 Feasible solutions 50—1 Feasible values 50—1 Feedback controller 57—13 Fejer’s theorem 8—10 Fekete’s Criterion 21—7 fermions 59—10 FFT see «Fast Fourier transform (FFT)» Fiedler vectors 36—1 36—4 36—7 Fiedler, Miroslav 66—1 to 66—15 Field ofrelational functions 23—2 Field ofvalues, convergence rates 41—16 Field ofvalues, numerical range 18—1 Fields P—3 Fill element 40—4 Fill graphs 40—14 Fill matrix 40—4 Fill-in, sparse matrix factorizations 49—3 Filter polynomial 44—6 Final class 54—5 Final subset 9—2 Fine, Morse decomposition 56—7 Finite dimensional, direct sum decompositions 2—5 Finite dimensional, nonassociative algebra 69—2 Finite dimensional, vector space 2—3 Finite energy 64—2 Finite impulse response (FIR), adaptive filtering 64—12 Finite impulse response (FIR), signal processing 64—2 64—3 Finite impulse response (FIR), Wiener filter 64—11 Finite Markov chain 54—2 Finite Markov chains 54—9 to 54—11 Finite power 64—5 Finite precision arithmetic 41—16 to 41—17 Finite time exponential growth rate 56—16 Finitely generated elements, Bezout domains 23—8 Finitely generated elements, max-plus algebra 25—2 Finitely generated ideals 23—2 FIR (finite impulse response), adaptive filtering 64—12 FIR (finite impulse response), signal processing 64—2 64—3 FIR (finite impulse response), Wiener filter 64—11 FIR Wiener filtering problem 64—10 First (population) canonical correlations and variates 53—7 First level radix 2 FFT 58—17 to 58—18 First, Mathematica software, matrices manipulation 73—13 First, Mathematica software, singular values 73—18 First, Mathematica software, vectors 73—3 Fischer’s Determinantal Inequality 8—10 Fischer’s inequality 14—11 Fixed point, linear dynamical systems 56—5 Fixed point, linearization 56—19 Fixed spaces 3—6 Flag manifolds 56—7 56—9 Flatten, Mathematica software, fundamentals 73—27 Flatten, Mathematica software, linear programming 73—24 Flatten, Mathematica software, matrices manipulation 73—14 Flexible algebra 69—10 Flip map 22—2 Floating point numbers 37—11 to 37—16 Floating point operation (flop), algorithms and efficiency 37—16 Floating point operation (flop), large-scale matrix computations 49—2 Floquet exponents 56—17 Floquet theory, dynamical systems 56—12 to 56—14 Floquet theory, random linear dynamical systems 56—15 to 56—16 Flow lattice 30—2 Flux balancing equation 60—10 to 60—13 fname command, Matlab software 71—10 71—11 FOM (Full Orthogonalization Method) 41—7 for loops, Matlab software 71—11 Ford-Fulkerson theorem 27—7 Forest, graphs 28—2 format short command, Matlab software 71—8 Formed space 67—5 Formulating linear programs 50—3 to 50—7 Formulation 50—3 to 50—7 Forward errors 37—18 37—20 Forward stability 37—18 Four (4)-cockades 30—4 Fourier analysis, discrete theory 58—8 to 58—17 Fourier analysis, fast Fourier transform 58—17 to 58—20 Fourier analysis, function/functional theory 58—2 to 58—8 58—12 Fourier analysis, fundamentals 58—1 Fourier coefficients 5—4 Fourier expansion 5—4 Fourier transforms, Green’s functions 59—10 Fourier transforms, Karle — Hauptman matrix 60—8 Frame 56—9 Frameticks, Mathematica software 73—27 Free algebras 69—18 Free distance 61—12 Free Lie algebra 70—2 Free variables 1—10 Freeware (software) 77—1 to 77—3 Frequency response 64—2 Frequency-domain analysis 57—5 to 57—6 Freund, Roland W. 49—1 to 49—15 Friedland, Shmuel 23—1 to 23—10 24—1 Friendship theorem 28—7 Frobenius inequality 14—13 Frobenius norm, eigenvalues 15—4 Frobenius norm, elementary analytic results 26—12 Frobenius norm, irreducible matrices 29—7 Frobenius norm, matrices function behavior 16—10 Frobenius norm, matrix norms 37—4 Frobenius norm, protein structure comparison 60—4 Frobenius norm, semidefinite programming 51—3 Frobenius norm, singular value decomposition 5—11 Frobenius norm, square matrices 27—6 29—11 Frobenius norm, unitarily invariant norms 17—6 Frobenius norm, unitary similarity 7—2 Frobenius norm, weak combinatorial invariants 27—6 Frobenius normal form 27—5 Frobenius reciprocity 68—9 68—10 Frobenius — Konigh theorem 27—4 Frobenius-Victory theorem 26—8 26—9 Front end, Mathematica software 73—1 Frontal/multifrontal methods 40—10 Frucht — Kantorovich Inequality 52—10 Full cones 8—10 Full level radix 2 FFT 58—18 to 58—19 Full Orthogonalization Method (FOM) 41—7 Full rank least squares problem 5—14 Full reorthogonalization procedure 42—20 to 42—21 Full-rank model 52—8 Fully indecomposable 27—3 to 27—4 Fulton studies 17—13 Function evaluation operator 62—5 to 62—6 Function/functional theory 58—2 to 58—8 58—12 Functional inequalities, irreducible matrices 9—5 Functional inequalities, reducible matrices 9—10 Functions of matrices, computational methods 11—9 to 11—12 Functions of matrices, cosine 11—7 to 11—8 Functions of matrices, exponential 11—5 to 11—6 Functions of matrices, fundamentals 11—1 Functions of matrices, logarithm 11—6 to 11—7 Functions of matrices, sign function 11—8 Functions of matrices, sine 11—7 to 11—8 Functions of matrices, square root 11—4 to 11—5 Functions of matrices, theory 11—1 to 11—4 Functions, Matlab software 71—11 Fundamental period 58—2 Fundamental subspaces 39—4 Fundamental tensor 13—25 Gale — Ryser Theorem 27—7 Galerkin condition, Arnoldi factorization 44—3 Galerkin condition, Krylov subspace projection 44—2 gallery command, Matlab software 71—5 Gantmacher studies 19—4 Gantmacher-Lyapunov theorem 26—14 Gaubert, Stephane 25—1 to 25—14 Gauss multipliers 38—7 Gauss transformations, Gauss elimination 38—7 Gauss transformations, sparse matrix factorizations 40—4 Gauss vectors 38—7 Gauss — Jordan elimination 1—7 to 1—9 Gauss — Markov model, least squares estimation 53—11 Gauss — Markov model, linear statistical models 52—8 Gauss — Markov theorem 52—11 Gauss — Newton method 51—8 Gauss — Seidel algorithm 41—14 Gauss — Seidel methods 41—3 to 41—4 Gaussian elimination see «LU factorizations» Gaussian elimination, algorithm efficiency 37—17 Gaussian elimination, bipartite graphs 30—7 Gaussian elimination, bisection and inverse iteration 42—15 Gaussian elimination, direct solution of linear systems 38—7 to 38—12 Gaussian elimination, fundamentals 1—7 to 1—9 Gaussian elimination, Karle — Hauptman matrix 60—8 Gaussian elimination, modeling and analyzing fill 40—10 Gaussian elimination, numerical stability and instability 37—20 37—21 Gaussian elimination, reordering effect 40—16 40—18 Gaussian elimination, sparse matrix factorizations 40—5 40—9 Gaussian Network Model 60—10 Gaussian properties 8—9 GCDD (greatest common divisor domain) 23—2 GEBAL LAPACK subroutine 43—3 General Inverse Eigenvalue Problem (GIEP) 34—8 General linear group, group representations 68—1 General linear group, matrix group 67—1 General Schur Theorem 43—2 Generalized cycle products 29—5 to 29—6 Generalized cycle, digraphs 29—2 Generalized eigenvalue problem 43—1 to 43—3 Generalized eigenvalues and eigenvectors 59—7 Generalized Euclidean Parallel Postulate 65—3 Generalized inverse 52—4
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