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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
Transient class matrices 9—15 Transient state 54—7 to 54—9 Transient substochastic matrices 9—15 Transition graphs 54—5 Transition matrix, coordinates and change of basis 2—10 Transition matrix, Markov chains 4—10 54—1 Transition probability 4—10 Transitive tournament matrices 27—9 Transpose, linear functionals and annihilator 3—8 Transpose, Maple software 72—3 72—5 72—9 Transpose, Mathematica software, eigenvalues 73—15 73—16 Transpose, Mathematica software, fundamentals 73—27 Transpose, Mathematica software, linear systems 73—23 Transpose, Mathematica software, matrices manipulation 73—13 Transpose, Mathematica software, matrix algebra 73—9 Transpose, matrices 1—4 Transpose-free quasi-minimal residual (TFQMR) linear systems of equations 49—14 Transvection 67—3 Tree of legs, simplexes 66—10 Trees, algebraic connectivity 36—4 to 36—6 Trees, digraphs 29—2 Trees, graphs 28—2 Trees, multiplicity lists 34—8 to 34—10 Trees, sign pattern 33—9 Trees, vines 34—15 TREVC LAPACK subroutine 43—6 TREXC LAPACK subroutine 43—7 Triangle inequality, inner product spaces 5—2 Triangle inequality, matrix norms 37—4 Triangle inequality, vector norms 37—2 Triangle inequality, vector seminorms 37—3 Triangle, points 65—2 Triangular back substitution 37—20 Triangular factorization 1—13 Triangular linear systems 38—5 to 38—7 Triangular matrices 10—4 Triangular property 35—2 Tridiagonal matrices 21—4 Tridiagonalization 42—5 to 42—9 TridiagonalMatrix, Mathematica software 73—6 TridiagonalSolve, Mathematica software 73—20 Trigonometric form 58—3 Trilinear aggregating technique 47—7 Trilinear maps 13—1 Trinomial distribution 52—4 Trivial face 26—2 Trivial factors 23—5 Trivial linear combination 2—1 Trivial perfect codes 61—9 Trivial representation 68—3 Tropical semiring 25—1 TRSEN LAPACK subroutine 43—7 TRSNA LAPACK subroutine 43—7 Truncated singular value decomposition 39—5 Truncated Taylor series 37—20 to 37—21 Truncation errors 37—12 Tsatsomeros, Michael 14—1 to 14—17 TSC (total signed compound) 46—8 Turbo codes 61—11 Turing machine 62—2 Turnpike theorem 25—9 Twisted factorization 42—17 Two(2)-design 32—2 Two(2)-norm 37—2 Two-bit Controlled-U gate 62—4 to 62—5 Two-bit gate 62—7 Two-dimensional column-major format 74—1 to 74—2 Two-sided Lanczos algorithm 41—7 UFD (unique factorization domain) 23—2 ULV decomposition 39—12 Unbounded region 50—1 Uncertainty 59—7 Uncontrollable modes 57—8 Uncorrelated vectors, data matrix 53—2 Uncorrelated vectors, random vectors 52—4 Underflow 37—11 to 37—12 Undirected graphs, digraphs 29—2 Undirected graphs, modeling and analyzing fill 40—10 Unicyclic graphs 36—3 Uniform distribution 52—2 Unimodular properties 23—5 Union, graphs 28—2 Unipotent, linear group ofdegree 67—1 Unique factorization domain (UFD) 23—2 Unique inertia 33—11 Unique normalization 23—3 to 23—4 Unit displacement rank matrix 46—9 Unit round 37—12 Unit triangular 1—4 Unit vectors 5—1 Unital characteristics 69—2 Unital hull 69—5 Unital matrices mappings 18—11 Unitary matrices, adjoint operators 5—6 Unitary matrices, orthogonality 5—3 Unitary matrices, pseudo-inverse 5—12 Unitary matrices, singular value decomposition 5—10 Unitary properties 5—2 Unitary properties, classical groups 67—5 Unitary properties, equivalence 7—2 Unitary properties, groups 67—5 Unitary properties, Hessenberg matrix 64—15 Unitary properties, invariance 17—2 18—6 Unitary properties, invariant norms 17—5 to 17—7 Unitary properties, linear operators 5—5 Unitary properties, Schrodinger’s equation 59—7 Unitary properties, similarity 7—2 Unitary similarity, invariant, numerical radius 18—6 Unitary similarity, matrices, special properties 7—1 to 7—5 Unitary similarity, transformation to upper Hessenberg form 43—4 Unitary similarity, upper Hessenberg form 43—4 Units, certain integral domains 23—2 Univariate linear model 53—11 Universal enveloping algebra 70—2 Universal factorization property 13—3 to 13—4 Universal property, Lie algebras 70—2 70—3 Universal property, symmetric and Grassmann tensors 13—14 to 13—15 Universal quantum gates 62—7 to 62—8 see Unknown vector 1—9 Unobservable modes 57—8 Unordered multiplicities 34—1 Unreduced Hessenberg matrix 44—3 Unreduced upper Hessenberg 43—3 Unsigned vectors 33—5 Unstability, linear differential-algebraic equations 55—14 Unstability, linear ordinary differential equations 55—10 Unstability, subspaces 56—3 Unsymmetric matrix eigensvalue techniques, dense Unsymmetric matrix eigensvalue techniques, matrix techniques 43—3 to 43—9 Unsymmetric matrix eigensvalue techniques, fundamentals 43—1 Unsymmetric matrix eigensvalue techniques, generalized eigenvalue problem 43—1 to 43—3 Unsymmetric matrix eigensvalue techniques, sparse matrix techniques 43—9 to 43—11 Updating, least squares solutions 39—8 to 39—9 Upper Collatz-Wielandt numbers 26—4 Upper Hessenberg matrices, Arnoldi factorization 44—3 Upper Hessenberg matrices, block diagonal and triangular matrices 10—4 Upper Hessenberg matrices, dense matrices 43—3 Upper Hessenberg matrices, form 43—3 43—4 Upper Hessenberg matrices, implicit restarting 44—6 Upper Hessenberg matrices, Krylov space methods 41—8 Upper Hessenberg matrices, linear systems of equations 49—13 Upper Hessenberg matrices, pseudospectra 16—3 Upper Hessenberg matrices, pseudospectra computation 16—11 Upper Hessenberg matrices, spectral estimation 64—15 Upper triangular properties, block diagonal and triangular matrices 10—4 Upper triangular properties, generalized eigenvalue problem 43—2 Upper triangular properties, linear matrix 38—5 Upper triangular properties, matrices 1—4 UpperDiagonalMatrix, Mathematica software 73—6 Upward eigenvalues 34—11 Upward multiplicity 34—11 URV decomposition 39—11 Valency, graphs 28—2 Valuation 36—7 Value, matrix games 50—18 Vandermonde determinant 4—3 Vandermonde matrices, factorizations 21—6 Vandermonde matrices, linear systems conditioning 37—11 Vandermonde matrices, Maple software 72—18 Vandermonde matrices, rank revealing decomposition 46—9 Vandermonde matrices, structured matrices 48—2 Vandermonde matrices, symmetric indefinite matrices 46—16 Vandermonde matrices, totally positive and negative matrices 21—3 Variables, pivoting 50—10 Variables, systems oflinear equations 1—9 Variance, principal component analysis 53—5 Variance, statistics and random variables 52—2 Variance-covariance matrix 52—3 Variety, simultaneous similarity 24—8 vars, Mathematica software, linear programming 73—24 vars, Mathematica software, linear systems 73—20 73—21 Vaserstein, Leonid N. 50—1 to 50—24 Vec-function 10—8 Vector generation, Maple software 72—2 to 72—3 Vector spaces,direct sum decompositions 2—5 Vector spaces,grading 70—8 Vector spaces,information retrieval 63—1 to 63—3 Vector spaces,linear independence 2—4 Vector, Maple software 72—1 72—2 Vector, Mathematica software 73—3 Vector-Matrixproducts, Maple software 72—6 VectorNorm, Mathematica software 73—27 VectorQ, Mathematica software 73—4 Vectors see specific type Vectors, balanced 33—5 Vectors, control theory 57—2 Vectors, Euclidean point space 66—1 Vectors, fundamentals 1—1 to 1—3 2—3 3—2 Vectors, Gauss elimination 38—7 Vectors, Google’s PageRank 63—11 Vectors, Maple software 72—2 to 72—4 Vectors, Mathematica software 73—3 to 73—5 Vectors, max-plus algebra 25—1 Vectors, multiply, spare matrices 43—10 Vectors, NMR protein structure determination 60—2 Vectors, norms, error analysis 37—2 to 37—3 Vectors, Perron — Frobenius theorem 26—2 Vectors, query 63—2 Vectors, seminorms, error analysis 37—3 to 37—4 Vectors, sign solvability 33—5 Vectors, space over 1—1 Vectors, spaces 1—2 Vectors, vector space method 63—2 Vectors, vector space method, Maple software 72—9 Vedell, Peter 60—13 Vertex coloring 28—9 Vertex independence number 28—9 Vertex-edge incidence matrix 28—7 to 28—8 Vertices, digraphs 29—1 Vertices, Euclidean simplexes 66—7 Vertices, graphs 28—1 Vertices, nonnegative and stochastic matrices 9—2 Vertices, phase 2 geometric interpretation 50—13 Vertices, stars 34—10 Vines 34—15 Volodin, Kimmo Vahkalahti Andrei 53—14 Volterra — Lyapunov stability 19—9 von Neumann, J. 50—24 Vorobyev — Zimmermann covering theorem 25—11 vpa command, Matlab software 71—17 71—19 Walk of length, digraphs 29—2 Walk of length, graphs 28—1 Walk-regular graphs 28—3 Walks, digraphs 29—2 Walks, irreducible classes 54—5 Walks, products 29—4 to 29—5 Walsh-Hadamard gate, quantum computation 62—3 Walsh-Hadamard gate, universal quantum gates 62—7 Walsh-Hadamard transform 62—10 Wang, Jenny 75—1 to 75—23 Wangsness, Amy 35—1 to 35—20 Wanless, Ian M. 31—1 to 31—13 Watkins, David S. 43—1 to 43—11 Watkins, William 32—1 to 32—12 Watson efficiency 52—9 52—10 52—13 Weak combinatorial invariants 27—1 27—5 Weak properties, cyclic of index 54—9 Weak properties, duality 51—6 Weak properties, expanding characteristics 9—8 9—11 Weak properties, Floquet theory 56—15 to 56—16 Weak properties, model 52—8 Weak properties, numerical stability 37—19 Weak properties, sign symmetric 19—3 Weak properties, unitarily invariant 18—6 web crawlers 63—9 Web searches 63—8 to 63—10 see Wedin theorem 15—7 Wehrfritz, B.A.F. 67—6 Weierstrauss preparation theorem 24—4 Weight characteristic, coding theory 61—2 Weight characteristic, convolutional codes 61—11 Weight characteristic, Fiedler vectors 36—7 Weight characteristic, max-plus algebra 25—2 Weight function, digraphs 29—2 Weight function, Fiedler vectors 36—7 Weight least squares problem 39—1 Weight space 70—7 Weighted bigraph 30—4 Weighted digraphs 29—2 Weighted graphs, algebraic connectivity 36—7 to 36—9 Weighted graphs, Fiedler vectors 36—7 Weiner, Paul 61—1 to 61—13 Well-conditioned data 37—7 Well-conditioned linear systems 37—10 Weyl character formula 70—9 Weyl group, BN structure 67—4 Weyl group, Lie algebra and modules 70—9 Weyl group, semisimple and simple algebras 70—4 Weyl inequalities, eigenvalues 14—4 Weyl inequalities, Hermitian matrices 8—3 8—4 Weyl’s theorem 70—8 Which, Mathematica software 73—8 while loops, Matlab software 71—11 White noise process 64—5 Wide-sense stationarysignals 64—4 Wiegmann studies 7—8 Wielandt-Hoffman theorem 37—21 Wiener deconvolution problem 64—10 Wiener filter 64—10 Wiener filtering 64—10 to 64—11 Wiener prediction problem 64—10 Wiener smoothing problem 64—10 Wiener vertex 34—2 Wiener — Hopf equations, linear prediction 64—7 64—8 Wiener — Hopf equations, Wiener filter 64—11 Wiens, Douglas P. 53—14 Wild problem 24—10 Wilkinson’s shift 42—9 Wilk’s Lambda 53—13 Wilson, Robert 70—1 to 70—10 Winograd, Coppersmith and, studies 47—9 Winograd’s commutative algorithm 47—2 Winograd’s formula 47—5 Wishart distribution 53—8 With, Mathematica software, fundamentals 73—26 With, Mathematica software, singular values 73—18 Within-groups matrix 53—6 Witsenhausen studies 30—9 Witt dimension 69—19 Witt index 67—5 67—6 Witt’s Lemma 67—6
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