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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
Max-cut problem 51—1 51—2 51—10 Max-plus algebra, asymptotics, matrix powers 25—8 to 25—9 Max-plus algebra, eigenproblem 25—6 to 25—8 Max-plus algebra, fundamentals 25—1 to 25—4 Max-plus algebra, linear independence and rank 25—12 to 25—14 Max-plus algebra, linear inequalities and projections 25—10 to 25—12 Max-plus algebra, maximal cycle mean 25—4 to 25—6 Max-plus algebra, permanent 25—9 to 25—10 Max-plus algebra, permanents 25—9 to 25—10 Max-plus Collatz-Wielandt formulas 25—4 to 25—5 Max-plus Cramer’s formula 25—13 Max-plus diagonal scaling 25—6 Max-plus eigenproblem 25—6 to 25—8 Max-plus permanent 25—9 to 25—10 Max-plus polynomial function 25—9 Max-plus semiring 25—1 Maximal cycle mean 25—4 to 25—6 Maximal ideal 23—2 Maximal rank 33—11 Maximal sign nonsingularity 33—3 Maximize, Mathematica software 73—23 73—27 Maximum absolute column sum norm 37—4 Maximum absolute row sum norm 37—4 Maximum distance separable (MDS) 61—5 Maximum distance separable (MDS) convolutional codes 61—12 Maximum entropy method 64—14 64—15 Maximum likelihood estimates 53—4 Maximum multiplicity 34—4 to 34—6 Maximum rank deficiency 34—4 Maxplus toolbox 25—6 Maxwell’s equations 59—2 McDonald studies 26—7 McLaurin expansion 23—9 McMillan degree 57—6 MDS (maximum distance separable) 61—5 MDS (maximum distance separable) convolutional codes 61—12 Mean square prediction error 64—7 Mean value 52—2 Mean vectors 52—3 Mean, multivariate normal inference 53—4 Mean, statistics and random variables 52—2 Measure of relative separation 17—7 Measured outputs 57—14 Mehrmann, Volker 55—1 to 55—16 Meini iteration 11—11 Meini, Beatrice 54—1 to 54—14 Menage number 31—6 Menger matrix, Euclidean simplexes 66—8 66—9 Menger matrix, fundamentals 66—12 Menger matrix, resistive electrical networks 66—15 Merging,matrix power asymptotics 25—8 Merging,nonnegative IEPs 20—8 mesh command, Matlab software 71—15 Mesh, Mathematica software 73—27 meshgrid command, Matlab software 71—14 Message blocks of length 61—1 Metabolites 60—10 Method ofCondensation 4—4 Metric dynamical systems 56—12 Metric multidimensional scaling 53—13 to 53—14 Metric net, simplexes 66—10 Metrics P—4 Meyer, Carl D. 63—1 to 63—14 MGS (modified Gram-Schmidt) process 44—4 Midpoint, affine spaces 65—2 Midpoint, Euclidean point space 66—2 MIEPs (multiplicative IEPs) 20—10 Mills, Mark 2—1 to 2—12 Min-plus semiring 25—1 Minimal connection 29—12 to 29—13 Minimal matrix norms 37—4 Minimal polynomials, convergence in gap 44—9 Minimal polynomials, eigenvalues and eigenvectors 4—6 Minimal polynomials, Krylov subspaces 49—6 Minimal rank 33—11 Minimal realization 57—6 Minimal Residual (MINRES) algorithm, convergence rates 41—14 to 41—15 Minimal Residual (MINRES) algorithm, Krylov space methods 41—4 41—6 41—10 Minimal sign-central matrices 33—17 Minimally chordal symmetric Hamiltonian 35—15 Minimally potentially stable 33—7 Minimax theorem 50—18 Minimize, Mathematica software, fundamentals 73—27 Minimize, Mathematica software, linear programming 73—23 73—24 Minimum co-cover 27—2 Minimum cover 27—2 Minimum deficiency algorithm 40—17 Minimum entropy controller 57—15 Minimum phase 64—2 Minimum rank 34—4 to 34—6 Minimum rank inertia 33—11 to 33—12 Minimum-norm least squares solution 39—1 Minors see «Principal minors» Minors, determinants 4—1 Minors, graphs 28—4 Minors, Mathematica software 73—10 73—11 MINRES (Minimal Residual) algorithm, convergence rates 41—14 to 41—15 MINRES (Minimal Residual) algorithm, Krylov space methods 41—4 41—6 41—10 Minus algebra 69—2 Mirsky theorem 15—6 Mixed strategies, matrix games 50—18 Mobius function 20—7 Model matrix 52—8 Models see specific model Models, fill, sparse matrix methods 40—10 to 40—13 Models, full-rank 52—8 Models, Gauss — Markov model 52—8 53—11 Models, LAPACK subroutine package 75—8 to 75—9 Models, linear statistical 52—1 to 52—15 Models, multivariate linear model 53—11 Models, multivariate statistical analysis 53—11 to 53—13 Models, Pade 49—14 49—15 Models, Pade model 49—14 Models, reduced-order model 49—14 Models, signal model 64—16 Models, univariate linear model 53—11 Modified Gram-Schmidt (MGS) process 44—4 Modified incomplete Cholesky decomposition 41—11 Modular arithmetic 72—12 to 72—13 Module, Mathematica software 73—26 Modules, group representations 68—2 Modules, Lie algebras 70—7 to 70—10 Modules, matrix representations 68—4 Molecular distance geometry problem 60—2 Moment generating function 53—3 Monic polynomials 23—2 Monotone class 27—7 to 27—8 Monotone vector norm 37—2 Mood studies 32—1 Moore — Penrose inverse, inverse patterns 33—12 33—13 Moore — Penrose inverse, least squares solutions 39—2 Moore — Penrose inverse, linear statistical models 52—12 Moore — Penrose inverse, Maple software 72—7 Moore — Penrose pseudo-inverse, extensions 16—13 Moore — Penrose pseudo-inverse, pseudo-inverse 5—12 Morgan studies 44—6 Morse decompositions, dynamical systems 56—7 to 56—9 Morse decompositions, Grassmannian and flag manifolds 56—9 to 56—10 Morse decompositions, robust linear systems 56—17 Morse sets 56—7 Morse spectrum 56—16 Most, Mathematica software, fundamentals 73—27 Most, Mathematica software, matrices manipulation 73—13 Most, Mathematica software, vectors 73—3 Motzkin and Taussky studies 7—8 Moufang identities 69—10 Moulton Plane 65—9 Mukhopadhyay, Kriti 60—13 Multi-bigraph 30—4 multidimensional arrays 71—1 to 71—3 Multigrid method 41—3 41—11 Multilinear algebra, alt multiplication 13—17 to 13—19 Multilinear algebra, antisymmetric maps 13—10 to 13—12 Multilinear algebra, associated maps 13—19 to 13—20 Multilinear algebra, decomposable tensors 13—7 Multilinear algebra, Grassmann tensors 13—12 to 13—17 Multilinear algebra, Hodge star operator 13—24 to 13—26 Multilinear algebra, inner product spaces 13—22 to 13—24 Multilinear algebra, linear maps 13—8 to 13—10 Multilinear algebra, multilinear maps 13—1 to 13—3 Multilinear algebra, orientation 13—24 to 13—26 Multilinear algebra, sym multiplication 13—17 to 13—19 Multilinear algebra, symmetric maps 13—10 to 13—12 Multilinear algebra, symmetric tensors 13—12 to 13—17 Multilinear algebra, tensor algebras 13—20 to 13—22 Multilinear algebra, tensor multiplication 13—17 to 13—19 Multilinear algebra, tensor products 13—3 to 13—7 13—8 13—22 Multilinear maps 13—1 to 13—3 Multinomial distribution 52—4 Multiple linear regression 52—8 Multiple relativelyrobust representations (MRRR) 42—15 to 42—17 Multiplication 69—1 see Multiplication algebra 69—5 Multiplicative D-stability 19—5 to 19—7 Multiplicative ergodic theorem 56—14 to 56—15 Multiplicative IEPs (MIEPs) 20—10 Multiplicative perturbation, eigenvalue problems 15—13 Multiplicative perturbation, polar decomposition 15—8 Multiplicative perturbation, singular value problems 15—15 Multiplicative preservers 22—7 to 22—8 Multiplicity lists see «Symmetric matrices» Multiplicity lists, double generalized stars 34—11 to 34—14 Multiplicity lists, eigenvalues 34—7 to 34—8 Multiplicity lists, fundamentals 34—1 to 34—2 Multiplicity lists, generalized stars 34—10 to 34—11 Multiplicity lists, maximum multiplicity 34—4 to 34—6 Multiplicity lists, minimum rank 34—4 to 34—6 Multiplicity lists, parter vertices 34—2 to 34—4 Multiplicity lists, stars, generalized 34—10 to 34—14 Multiplicity lists, trees 34—8 to 34—10 Multiplicity lists, vines 34—15 Multiplicity, algebraic connectivity 36—10 to 36—11 Multiplicity, characters 68—6 Multiplicity, composition 13—13 Multiplicity, max-plus permanent 25—9 Multiplicity, singular value decomposition 45—1 Multiset P—4 to P—5 Multivariate Gauss-Markov theorem 53—12 Multivariate linear model 53—11 Multivariate normal distribution, multivariate statistical analysis 53—3 to 53—5 Multivariate normal distribution, positive definite matrices 8—9 Multivariate statistical analysis, canonical correlations and variates 53—7 Multivariate statistical analysis, correlations and variates 53—7 to 53—8 Multivariate statistical analysis, data matrix 53—2 to 53—3 Multivariate statistical analysis, discriminant coordinates 53—6 Multivariate statistical analysis, estimation, correlations and variates 53—7 to 53—8 Multivariate statistical analysis, fundamentals 53—1 to 53—2 Multivariate statistical analysis, inference, multivariate normal 53—4 to 53—5 Multivariate statistical analysis, least squares estimation 53—11 to 53—12 Multivariate statistical analysis, matrix quadratic forms 53—8 to 53—11 Multivariate statistical analysis, metric multidimensional scaling 53—13 to 53—14 Multivariate statistical analysis, models 53—11 to 53—13 Multivariate statistical analysis, multivariate normal distribution 53—3 to 53—5 Multivariate statistical analysis, principal component analysis 53—5 to 53—6 Multivariate statistical analysis, statistical inference 53—12 to 53—13 Murakami, Lucia I. 69—1 to 69—25 MUSIC algorithm 64—17 N-cycle matrices 48—2 Nagy, Kamm and, studies 48—9 naming conventions 76—3 to 76—4 narin command, Matlab software 71—12 narout command, Matlab software 71—12 Narrow sense Bose — Chadhuri — Hocquenghem (BCH) code 61—8 Narrow-band signals 64—16 Natural norms 37—4 Natural ordering 41—2 Near breakdown 49—8 Nearby floating point numbers 37—13 Nearest-neighbor decoding 61—2 Nearly decomposable 27—3 Nearly reducible matrices 29—12 to 29—13 Nearly sign non-singularity 33—3 Nearly sign-central matrices 33—17 Negative definite properties 12—3 12—8 Negative half-life 13—24 Negative orientation 13—24 Negative semi-definite properties, Hermitian forms 12—8 Negative semi-definite properties, symmetric bilinear forms 12—3 Negative semistability 33—7 Negative stability, sign pattern matrices 33—7 Negative stability, stability 19—3 Negative subdivision 20—8 Negative vertices 36—7 Neighbors, graphs 28—2 Nested basis 49—5 Nested dissection ordering 40—16 to 40—17 Net trace 20—7 Neubauer, Michael G. 32—1 to 32—12 Neumann boundary conditions 59—10 Neumann series 14—16 Neumann, Michael 5—1 to 5—16 Newton iteration 11—11 Newton-Schultz iteration 11—12 Newton’s law 59—1 Newton’s method, interior point methods 50—24 Newton’s method, numerical methods, PIEPs 20—11 Newton’s method, primal-dual interior point algorithm 51—8 Newton’s method, total least squares problem 48—9 Ng, Esmond G. 40—1 to 40—18 Ng, Michael 48—1 to 48—9 Nielsen, Hans Bruun 39—1 to 39—12 Nil algebra 69—5 Nil ideal properties 69—5 Nil radical algebras 69—5 Nil-semisimple algebras 69—5 Nilpotence, alternative algebras 69—10 Nilpotence, general properties 69—5 Nilpotence, idempotence 2—12 Nilpotence, invariant subspaces 3—6 Nilpotence, reducible matrices 9—11 to 9—12 Nilpotency index 69—5 Nilpotent radical algebras 69—6 Nodes, digraphs 29—1 Noise subspace 64—16 Noisy channel 61—2 Noisy transmission 61—2 Non-Hermitian case 49—12 Non-Hermitian Lanczos algorithm 41—7 Non-Hermitian problems 41—7 to 41—11 Non-optimal Krylov space methods 41—7 to 41—11 Nonassociative algebra 69—3 see Nonassociative algebra, Akivis algebra 69—16 to 69—17 Nonassociative algebra, alternative algebras 69—10 to 69—12 Nonassociative algebra, composition algebras 69—8 to 69—10 Nonassociative algebra, computational methods 69—20 to 69—25 Nonassociative algebra, fundamentals 69—1 to 69—4 Nonassociative algebra, Jordan algebras 69—12 to 69—14 Nonassociative algebra, Malcev algebras 69—16 to 69—17 Nonassociative algebra, noncommutative Jordan algebras 69—14 to 69—16 Nonassociative algebra, power associative algebras 69—14 to 69—16 Nonassociative algebra, properties 69—4 to 69—8 Nonassociative algebra, right alternative algebras 69—14 to 69—16 Nonassociative algebra, Sabinin algebra 69—16 to 69—17 Nonbasic variables 50—10 Noncentral distribution 53—3 Noncentral F-distribution 53—3 Noncollinear points 65—2 Noncommutative algorithms 47—2 Noncommutative Jordan algebra 69—14 Noncommutative Jordan algebras 69—14 to 69—16
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