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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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Balanced Boolean function, Deutsch-Jozsa problem 62—9 Balanced Boolean function, Deutsch’s problem 62—8 Balanced column signing 33—5 Balanced matrices, D-optimal matrices 32—12 Balanced matrices, nonsquare case 32—5 Balanced row signing 33—5 Balanced vectors 33—5 Banded matrices 41—2 Banding, Toeplitz matrices 16—6 Bandlimited random signals 64—5 Bapat, Ravindra 25—1 to 25—14 Barely L-matrices 33—5 Barioli, Francesco 3—1 to 3—9 Barker and Schneider studies 26—3 Barrett, Wayne 8—1 to 8—12 Barvinok rank 25—13 Barycentric coordinates 66—8 Bases, Bezout domains 23—8 Bases, complex sign and ray patterns 33—14 Bases, component, linear skew product flows 56—11 Bases, coordinates 2—10 to 2—12 Bases, induced, symmetric and Grassmann tensors 13—15 Bases, LTI systems 57—7 Bases, orthogonality 5—3 Bases, semisimple and simple algebras 70—4 Bases, similarity 3—4 Bases, vector spaces 2—3 to 2—4 Basic class of P 9—7 Basic variable 1—10 Bauer-Fike theorem, eigenvalue problems 15—2 Bauer-Fike theorem, pseudospectra 16—2 to 16—3 BCG/BiCG (biconjugate gradient) algorithm, Krylov space methods 41—7 41—10 BCG/BiCG (biconjugate gradient) algorithm, linear systems of equations 49—13 BCG/BiCG (biconjugate gradient) algorithm, preconditioners 41—12 BCH (Bose-Chadhuri-Hocquenghem) code 61—8 61—9 Beattie, Christopher 38—1 to 38—17 Belitskii reduction 24—10 Benner, Peter 57—1 to 57—17 Bernoulli random variables 52—2 Bernstein-Vazirani problem 62—11 to 62—13 Bessel’s inequality 5—4 Best approximation theorem 5—7 Best linear approximation 50—20 Best linear unbiased estimate (BLUE) 39—2 Best linear unbiased estimator 52—9 Best PSD approximation 17—13 Best rank k approximation 17—12 to 17—13 Best unitary approximation 17—13 Between-groups matrix 53—6 Bezout domains, certain integral domains 23—2 Bezout domains, matrices over integral domains 23—8 to 23—9 Bezout domains, matrix equivalence 23—6 Bhatia studies 17—13 Biacyclic matrices 46—8 Biadjacency matrix 30—1 Biclique cover 30—8 Biclique cover number 30—8 Biclique partition 30—8 Biclique partition number 30—8 Biclique, bipartite graphs 30—8 Biconjugate gradient (BCG/BiCG) algorithm, Krylov space methods 41—7 41—10 Biconjugate gradient (BCG/BiCG) algorithm, linear systems of equations 49—13 Biconjugate gradient (BCG/BiCG) algorithm, preconditioners 41—12 Bideterminants 25—13 Bidiagonal singular values by bisection 45—9 Bidual space 3—8 Bigraphs 40—10 40—11 see Bilinear forms, alternating forms 12—5 to 12—6 Bilinear forms, fundamentals 12—1 to 12—3 Bilinear forms, Jordan algebras 69—13 Bilinear forms, symmetric form 12—1 to 12—5 Bilinear maps 13—1 Bilinear noncommutative algorithms 47—2 Bimodule algebras 69—6 Binary even weight codes 61—4 Binary Golay code 61—8 61—9 Binary linear block code (BLBC) 61—3 Binary matrices, permanents 31—5 to 31—7 Binary symmetric channel 61—3 to 61—4 Binary trees 34—15 Binet-Cauchy identity 25—13 Binet-Cauchy theorem 31—2 Bini, Dario A. 47—1 to 47—10 Binomial distribution 52—4 Binomial, Mathematica software 73—26 Biological sciences applications 60—1 to 60—13 Biomolecular modeling, flux balancing equation 60—10 to 60—13 Biomolecular modeling, fundamentals 60—1 60—13 Biomolecular modeling, Karle-Hauptman matrix 60—7 to 60—9 Biomolecular modeling, mapping 60—2 to 60—4 Biomolecular modeling, metabolic network simulation 60—10 to 60—13 Biomolecular modeling, NMR protein structure determination 60—2 to 60—4 Biomolecular modeling, protein motion modes 60—9 to 60—10 Biomolecular modeling, protein structure comparison 60—4 to 60—7 Biomolecular modeling, x-ray crystallography 60—7 to 60—9 Biorthogonal pair of bases 66—5 Biorthogonalization singular value decomposition 45—11 Bipartite graphs, factorizations 30—8 to 30—10 Bipartite graphs, fill-graph 30—4 Bipartite graphs, fundamentals 30—1 to 30—3 Bipartite graphs, graphs 28—2 Bipartite graphs, matrices 30—4 to 30—7 Bipartite graphs, modeling and analyzing fill 40—10 Bipartite graphs, rank revealing decomposition 46—8 Bipartite sign pattern matrices 33—9 Birepresentations 69—6 Birkhoff’s theorem 27—11 Bisection method 42—14 to 42—15 Bit flipping algorithm 61—11 Bit quantum gate 62—2 Black-box 66—13 Black-box matrix 66—13 to 66—15 Bland’s rule 50—12 50—13 BLAS subroutine package, fundamentals 74—1 to 74—7 BLAS subroutine package, method comparison 42—21 BLBC (binary linear block code) 61—3 Block code of length 61—1 Block diagonal matrices 10—4 to 10—6 Block lower triangular matrices 10—4 Block matrices, partitioned matrices 10—1 to 10—3 Block matrices, structured matrices 48—3 Block positive semidefinite matrices 17—9 Block triangular matrices, inequalities 17—9 Block triangular matrices, partitioned matrices 10—4 to 10—6 Block upper triangular matrices 10—4 Block, graphs and digraphs 35—2 Block-clique 35—2 Block-Toeplitz matrices 48—3 Block-Toeplitz-Toeplitz-Block (BTTB) matrices 48—3 BlockMatrix, Mathematica software 73—13 Blocks, square case 32—2 Bloomfield-Watson efficiency 52—9 52—10 52—13 Bloomfield-Watson Trace Inequality 52—10 52—13 Bloomfield-Watson-Knott Inequality 52—10 52—13 BLUE (best linear unbiased estimate) 39—2 BN structure, matrix groups 67—4 to 67—5 Bochner’s theorem 8—10 8—11 8—12 Boolean properties, algebra 30—8 Boolean properties, bipartite graphs 30—8 30—9 Boolean properties, Deutsch-Jozsa problem 62—9 Boolean properties, Deutsch’s problem 62—8 Boolean properties, fast matrix multiplication 47—10 Boolean properties, matrices 30—8 47—10 Boolean properties, rank 30—8 30—9 Borel subgroup 67—4 67—5 Borobia, Alberto 20—1 to 20—12 Bose-Chadhuri-Hocquenghem (BCH) code 61—8 Bose-Mesner algebra 28—11 Bosons 59—10 Bottleneck matrices 36—4 Boundaries, fundamentals P—1 Boundaries, interior point methods 50—23 Boundaries, numerical range 18—3 to 18—4 Bounded properties 9—11 Box, Euclidean spaces 66—10 Branches, matrix similarities 24—1 Branches, multiplicities and parter vertices 34—2 Brauer theorem 14—6 Bregman’s bound 31—7 Bremmer, Murray R. 69—1 to 69—25 Brent, R. 47—5 Brin, Sergey 54—4 63—9 63—10 Browne’s theorem 14—2 Brualdi, Richard A. 27—1 to 27—12 BTTB (Block-Toeplitz-Toeplitz-Block) matrices 48—3 bucky command, Matlab software 71—11 Built-in functions, Matlab software 71—4 to 71—5 Bulge 42—10 43—5 Bunch-Parlett factorization 46—14 Burnside’s Vanishing theorem 68—6 Businger-Golub pivoting, preconditioned Jacobi SVD algorithm 46—5 Businger-Golub pivoting, rank revealing decompositions 46—9 Butterfly relations 58—18 58—20 Byers, Ralph 37—1 to 37—21 Cameron, Peter J. 67—1 to 67—7 Canonical angle and canonical angle matrix 15—2 Canonical angles 17—15 Canonical correlations and variates, multivariate statistical analysis 53—7 Canonical correlations and variates, singular values 17—15 Canonical forms, eigenvectors, generalized 6—2 to 6—3 Canonical forms, elementary divisors 6—8 to 6—11 Canonical forms, fundamentals 6—1 to 6—2 Canonical forms, invariant factors 6—12 to 6—14 Canonical forms, Jordan canonical form 6—3 to 6—6 Canonical forms, linear programming 50—7 50—7 Canonical forms, Maple software 72—15 to 72—16 Canonical forms, rational canonical forms 6—8 to 6—11 6—12 Canonical forms, real-Jordan canonical form 6—6 to 6—8 Canonical forms, Smith normal form 6—11 to 6—12 Canonical variates 53—6 Cartan matrix 70—4 Cartan’s Criterion for Semisimplicity 70—4 Cartesian coordinates 55—3 Cartesian decomposition 17—11 Cartesian product 13—11 to 13—12 Cassini, ovals of 14—6 14—6 cat command, Matlab software 71—2 Cauchy boundary conditions 55—3 Cauchy integral 11—2 Cauchy interlace property 42—20 Cauchy matrices, rank revealing decompositions 46—9 Cauchy matrices, structured matrices 48—2 Cauchy matrices, symmetric indefinite matrices 46—16 Cauchy matrices, totally positive and negative matrices 21—4 Cauchy-Binet formula, determinants 4—4 4—5 Cauchy-Binet formula, matrix equivalence 23—6 Cauchy-Binet Identity 21—2 Cauchy-Binet inequalities 14—10 Cauchy-Schwartz inequality, inner product spaces 5—1 5—2 Cauchy-Schwartz inequality, vector norms 37—3 Causal part, Wiener filtering 64—10 Causal signal processing 64—2 Cayley numbers, nonassociative algebra 69—4 Cayley numbers, standard forms 22—4 Cayley-Dickson algebra, alternative algebra 69—11 69—12 Cayley-Dickson algebra, Jordan algebras 69—16 Cayley-Dickson algebra, Malcev algebras 69—17 Cayley-Dickson algebra, nonassociative algebra 69—4 Cayley-Dickson algebra, power associative algebras 69—15 Cayley-Dickson doubling process 69—4 Cayley-Dickson matrix algebra 69—9 Cayley-Hamilton theorem 4—8 Cayley’s formula 7—6 Cayley’s Transform 7—6 CCS (compressed column storage) scheme 40—3 Cell bracket, Mathematica software 73—2 Cells, Mathematica software 73—2 Censoring, Markov chains 54—11 Center 69—5 Center subspaces 56—3 Centering matrix 52—4 Central algebra 69—5 Central controller 57—15 Central distribution 53—3 Central force motion 59—4 to 59—5 Central matrices 33—17 Central Moufang identity 69—10 Central path 51—8 Central vertex 34—10 Centroid 69—5 Certain integral domains 23—1 to 23—4 CG (Conjugate Gradient) algorithm, convergence rates 41—14 to 41—15 CG (Conjugate Gradient) algorithm, Krylov space methods 41—4 41—6 CGS (classical Gram-Schmidt) scheme 44—3 to 44—4 see CGS (Conjugate Gradient Squared) algorithm 41—8 Chain exponent 56—16 Chain recurrence 56—7 to 56—9 Chain recurrent component 56—7 Chain recurrent set 56—7 Chain transitive 56—7 Change of basis, coordinates 2—10 to 2—12 Change of basis, LTI systems 57—7 Change of basis, similarity 3—4 Change-of-basis matrix 2—10 Channels, coding theory 61—2 Character table 68—7 Characteristic equation 43—2 Characteristic polynomial function 25—9 Characteristic polynomial, adjacency matrix 28—5 Characteristic polynomial, fast matrix multiplication 47—10 Characteristic polynomial, generalized eigenvalue problem 43—2 Characteristic polynomials 4—6 Characteristic vector 30—8 Characteristic vertex 36—4 CharacteristicPolynomial, Maple software, eigenvalues and CharacteristicPolynomial, Maple software, eigenvectors 72—11 72—12 CharacteristicPolynomial, Maple software, matrix stability 72—21 CharacteristicPolynomial, Maple software, nonlinear algebra 72—14 CharacteristicPolynomials, Mathematica software 73—14 Characterizations, singular values 17—1 to 17—3 Characters, grading 70—9 Characters, group representations 68—5 to 68—6 Characters, restriction 68—8 to 68—10 Characters, table 68—6 to 68—8 Chebyshev polynomial, convergence rates 41—15 Chebyshev polynomial, polynomial restarting 44—6 Chebyshev polynomial, rook polynomials 31—11 Checkerboard partial order 21—9 Chemical flux 60—10 Cholesky algorithm 46—11 Cholesky decomposition, preconditioners 41—12 41—13 Cholesky decomposition, symmetric factorizations 38—15 38—16 Cholesky factor, modeling and analyzing fill 40—13 Cholesky factor, positive definite matrices 46—12 Cholesky factor, QR factorization 39—9 Cholesky factor, reordering effect 40—16 40—18 Cholesky factorization with pivoting 46—10 Cholesky factorization, extensions 16—13 Cholesky factorization, least squares algorithms 39—7 Cholesky factorization, linear prediction 64—8 Cholesky factorization, positive definite matrices 8—7 46—13 Cholesky factorization, sparse matrices 49—3 to 49—5 Cholesky factorization, sparse matrix factorizations 49—3 Cholesky factorization, symmetric factorizations 38—15 Cholesky-like factorization 8—9 CholeskyDecomposition, Mathematica software 73—18 73—27 Chop, Mathematica software 73—25 Chordal bipartite graph, bipartite graphs 30—1 Chordal distance, eigenvalue problems 15—10 Chordal graph, bipartite graphs 30—1 Chordal graphs 35—2
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