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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
31—8 35—12 to 35—13 (MRRR) multiple relatively robust representations 42—15 to 42—17 1hs, Mathematica software 73—20 Abelian, Lie algebras 70—2 Abs, Mathematica software 73—26 Absolute bound 28—11 Absolute errors, conditioning and condition numbers 37—7 Absolute errors, floating point numbers 37—13 37—16 Absolute irreducibility 67—1 Absolute matrix norms 37—4 Absolute values 17—1 Absolute vector norm 37—2 Absolute, simple graphs 36—9 to 36—10 Absorbing, irreducible classes 54—5 Absorbing, vector norms 37—3 Absorbing, vector seminorms 37—4 Access equivalence irreducible classes 54—5 Access equivalence, irreducible matrices 29—6 29—7 Access equivalence, max-plus eigenproblem 25—6 Access equivalence, nonnegative and stochastic matrices 9—2 Action, group representations 68—2 Active branch, algebraic connectivity 36—5 Active constraints 51—1 Acyclic matrices multiplicative D-stability 19—6 Acyclic matrices rank revealing decompositions 46—9 Ad-nilpotency 70—4 Ad-semisimple linear transformation 70—4 Adaptive filtering, signal processing 64—12 to 64—13 Addition 1—1 1—3 Additive coset 2—5 Additive D-stability 19—7 to 19—8 Additive identity axiom 1—1 Additive IEPs (AIEPs) 20—10 Additive inverse axiom 1—1 Additive preservers 22—7 to 22—8 Adjacency convex set points 50—13 Adjacency digraphs 29—3 to 29—4 Adjacency graphs 28—5 to 28—7 Adjacency Hermitian matrices 8—2 Adjacency linear preservers 22—7 Adjacency vertices 28—2 Adjoint linear transformation 51—3 Adjoint map, Lie algebras 70—2 Adjoints of linear operators, inner product spaces 5—5 to 5—6 Adjoints of linear operators, semidefinite programming 51—3 Adjoints, inner product spaces 13—22 Adjugates, determinants 4—3 Adjusting random vectors 52—4 Admissibility, control theory 57—2 Admittance matrix 28—7 Advanced linear algebra, bilinear forms 12—1 to 12—9 Advanced linear algebra, cone invariant departure, matrices 26—1 to 26—14 Advanced linear algebra, equalities, matrices 14—1 to 14—17 Advanced linear algebra, functions of matrices 11—1 to 11—12 Advanced linear algebra, inequalities, matrices 14—1 to 14—17 Advanced linear algebra, inertia, matrices 19—1 to 19—10 Advanced linear algebra, integral domains, matrices over 23—1 to 23—10 Advanced linear algebra, inverse eigenvalue problems 20—1 to 20—12 Advanced linear algebra, linear preserver problems 22—1 to 22—8 Advanced linear algebra, matrix equalities and inequalities 14—1 to 14—17 Advanced linear algebra, matrix perturbation theory 15—1 to 15—16 Advanced linear algebra, matrix stability and inertia 19—1 to 19—10 Advanced linear algebra, max-plus algebra 25—1 to 25—14 Advanced linear algebra, multilinear algebra 13—1 to 13—26 Advanced linear algebra, numerical range 18—1 to 18—11 Advanced linear algebra, perturbation theory, matrices 15—1 to 15—16 Advanced linear algebra, pseudospectra 16—1 to 16—15 Advanced linear algebra, quadratic forms 12—1 to 12—9 Advanced linear algebra, sesquilinear forms 12—1 to 12—9 Advanced linear algebra, similarity of matrix families 23—1 to 23—10 Advanced linear algebra, singular values and singular value inequalities 17—1 to 17—15 Advanced linear algebra, stability, matrices 19—1 to 19—10 Advanced linear algebra, total negativity, matrices 21—1 to 21—12 Advanced linear algebra, total positivity, matrices 21—1 to 21—12 Affine algebraic variety 24—8 Affine function 50—1 Affine parameterized IEPs (PIEPs) 20—10 to 20—12 Affine subspace determination 65—2 Affine-independence 65—2 AIEPs (additive IEPs) 20—10 Aissen studies 21—12 Aitken estimator 52—8 Akian, Marianne 25—1 to 25—14 Akivis algebra 69—16 to 69—17 Albert algebra 69—4 69—14 Alexandroff inequality 25—10 Alexandrov’s inequality 31—2 Algebra P—1 Algebra applications see also «Nonassociative algebra» Algebra applications, group representations 68—1 to 68—11 Algebra applications, Lie algebras 70—1 to 70—10 Algebra applications, matrix groups 67—1 to 67—7 Algebra applications, nonassociative algebra 69—1 to 69—25 Algebraic aspects, least squares solutions 39—4 to 39—5 Algebraic connectivity, absolute, simple graphs 36—9 to 36—10 Algebraic connectivity, Fiedler vectors 36—7 to 36—9 Algebraic connectivity, generalized Laplacian 36—10 to 36—11 Algebraic connectivity, matrix representations 28—7 Algebraic connectivity, multiplicity 36—10 to 36—11 Algebraic connectivity, simple graphs 36—1 to 36—4 36—9 Algebraic connectivity, trees 36—4 to 36—6 Algebraic connectivity, weighted graphs 36—7 to 36—9 Algebraic eigenvalues 25—9 see Algebraic function, matrix similarities 24—1 Algebraic geometric Goppa (AG) code 61—10 Algebraic multigrid, preconditioners 41—11 Algebraic multiplicity 4—6 Algebraic Riccati equation (ARE) 57—10 57—12 Algorithms see specific algorithm Algorithms, Arbitrary Precision Approximating (APA) 47—6 Algorithms, Arnoldi 41—7 Algorithms, BiCGSTAB 41—8 Algorithms, biconjugate gradient (BCG/BiCG) 41—7 49—13 Algorithms, bilinear noncommutative 47—2 Algorithms, bit flipping algorithm 61—11 Algorithms, Conjugate Gradient (CG) 41—4 41—6 Algorithms, conjugate gradient squared (CGS) 41—8 Algorithms, Denardo 25—8 Algorithms, error analysis 37—16 to 37—17 Algorithms, ESPRIT 64—17 Algorithms, Euclid’s 23—2 Algorithms, fast matrix multiplication 47—2 to 47—7 Algorithms, Full Orthogonalization Method (FOM) 41—7 Algorithms, Generalized Minimal Residual (GMRES) 41—7 49—13 Algorithms, Lanczos algorithm 41—4 to 41—5 Algorithms, least squares solutions 39—6 to 39—7 Algorithms, left-preconditioned BiCGSTAB algorithm 41—12 Algorithms, Levinson-Durbin algorithm 64—8 Algorithms, Minimal Residual (MINRES) 41—4 41—6 Algorithms, MUSIC 64—17 Algorithms, non-Hermitian Lanczos algorithm 41—7 Algorithms, noncommutative 47—2 Algorithms, policy iteration 25—7 Algorithms, power algorithm 25—7 Algorithms, preconditioned conjugate gradient (PCG) 41—13 Algorithms, quasi-minimal residual (QMR) 41—8 49—13 Algorithms, restarted GMRES algorithm 41—7 Algorithms, singular value decomposition 45—4 to 45—12 Algorithms, transpose-free quasi-minimal residual (TFQMR) 49—14 Algorithms, two-sided Lanczos algorithm 41—7 All-ones matrix 52—4 Allowing characteristics, random vectors 52—4 Allowing characteristics, sign-pattern matrices 33—9 to 33—11 Alphabet, coding theory 61—1 Alt multiplication 13—17 to 13—19 Alternate path, single arc 35—14 Alternating bilinear forms 12—5 to 12—6 Alternative algebras 69—2 69—10 Alternative bimodule 69—10 Alternator 13—12 AMG code 41—12 Analysis applications, control theory 57—1 to 57—17 Analysis applications, differential equations 55—1 to 55—16 Analysis applications, dynamical systems 56—1 to 56—21 Analysis applications, Fourier analysis 58—1 to 58—20 Analysis applications, LTI systems 57—7 to 57—10 Analysis applications, stability 55—1 to 55—16 Analytical similarity 24—1 Analyzing fill 40—10 to 40—13 Angles, inner product spaces 5—1 Annihilator 3—8 to 3—9 Anti-identity matrices 48—2 Anticommutative algebra 69—2 Anticommutativity 70—2 Anticommutator 69—3 Antisymmetric maps 13—10 to 13—12 Antisymmetry 12—5 Aperiodicity, characterizing 9—3 Aperiodicity, irreducible classes 54—5 Aperiodicity, irreducible matrices 9—3 Aperiodicity, reducible matrices 9—7 Append, Mathematica software, linear systems 73—23 Append, Mathematica software, matrices manipulation 73—13 Append, Mathematica software, vectors 73—3 AppendColumns, Mathematica software 73—13 Appending, vertices 36—3 AppendRows, Mathematica software 73—13 Applications, algebra, group representations 68—1 to 68—11 Applications, algebra, Lie algebras 70—1 to 70—10 Applications, algebra, matrix groups 67—1 to 67—7 Applications, algebra, nonassociative algebra 69—1 to 69—25 Applications, analysis, control theory 57—1 to 57—17 Applications, analysis, differential equations 55—1 to 55—16 Applications, analysis, dynamical systems 56—1 to 56—21 Applications, analysis, Fourier analysis 58—1 to 58—20 Applications, analysis, stability 55—1 to 55—16 Applications, biological sciences 60—1 to 60—13 Applications, computer science, coding theory 61—1 to 61—13 Applications, computer science, information retrieval 63—1 to 63—14 Applications, computer science, quantum computation 62—1 to 62—19 Applications, computer science, signal processing 64—1 to 64—18 Applications, computer science, Web searches 63—1 to 63—14 Applications, fast matrix multiplication 47—9 to 47—10 Applications, geometry, Euclidean geometry 66—1 to 66—15 Applications, geometry, geometry 65—1 to 65—9 Applications, optimization, linear programming 50—1 to 50—24 Applications, optimization, semidefinite programming 51—1 to 51—11 Applications, physical sciences 59—1 to 59—11 Applications, probability and statistics, linear statistical models 52—1 to 52—15 Applications, probability and statistics, Markov chains 54—1 to 54—14 Applications, probability and statistics, multivariate statistical analysis 53—1 to 53—14 Applications, probability and statistics, random vectors 52—1 to 52—15 Applications, semidefinite programming 51—9 to 51—11 Apply, Mathematica software 73—3 73—5 73—27 Approximate Jordan form, Maple software 72—15 Approximate prescribed-line-sum scalings 9—21 to 9—22 Approximation, fast matrix multiplication 47—6 to 47—7 Approximation, linear programming 50—20 to 50—23 Approximation, orthogonal projection 5—7 ArbitraryPrecision Approximating (APA) algorithms 47—6 ArcSin, Mathematica software 73—26 ARE see «Algebraic Riccati equation (ARE)» Arithmetic Euclidean vector space 66—1 Arm, stars 34—10 Arnold Hypothesis, Strong 28—9 28—10 Arnoldi algorithm 41—7 41—8 Arnoldi decomposition 16—11 Arnoldi factorization, implicitly restarted Arnoldi method 44—2 to 44—4 Arnoldi factorization, pseudospectra 16—3 Arnoldi matrices 49—11 Arnoldi method see «Implicitly restarted Arnoldi method (IRAM)» Arnoldi method, eigenvalue computations 49—12 Arnoldi method, implicit restarting 44—6 Arnoldi method, large-scale matrix computations 49—10 to 49—11 Arnoldi method, sparse matrices 43—9 43—11 Arnoldi vectors, Arnoldi factorization 44—3 Arnoldi vectors, Arnoldi process 49—11 ARPACK subroutine package, computational modes 76—8 to 76—9 ARPACK subroutine package, directory structure and contents 76—3 ARPACK subroutine package, fundamentals 76—1 to 76—2 76—4 ARPACK subroutine package, Lanczos methods 42—21 ARPACK subroutine package, Matlab’s EIGS 76—9 to 76—10 ARPACK subroutine package, naming conventions 76—3 to 76—4 ARPACK subroutine package, precisions 76—3 to 76—4 ARPACK subroutine package, pseudospectra computation 16—12 ARPACK subroutine package, reverse communication 76—2 ARPACK subroutine package, setup of problem 76—5 to 76—7 ARPACK subroutine package, sparse matrices 43—9 ARPACK subroutine package, types 76—3 to 76—4 ARPACK subroutine package, use 76—7 to 76—8 Array arithmetic, Maple software 72—8 Array, Maple software 72—1 72—2 Array, Mathematica software, matrices 73—6 Array, Mathematica software, vectors 73—3 73—4 ArrayPlot, Mathematica software, fundamentals 73—27 ArrayPlot, Mathematica software, matrices 73—7 73—9 ArrayRules, Mathematica software 73—6 Arrays, Fourier analysis 58—2 Arrays, manifold 64—16 Arrays, Maple software 72—8 to 72—9 Arrays, response vector 64—16 Arrays, response vector, Maple software 72—8 72—9 Arrival estimation direction 64—15 to 64—18 Arrow, Mathematica software 73—5 Artin’s theorem 69—3 69—11 AspectRatio, Mathematica software 73—27 Assignment polytope 27—10 Associated divisor 61—10 Associated linear programming 50—14 Associated maps 13—19 to 13—20 Association schemes, graphs 28—11 to 28—12 Associations, generalized stars 34—11 Associative algebra 69—2 Associative center 69—5 Associative enveloping algebra 69—13 Associative nucleus 69—5 Associativity axiom 1—1 1—2 Associator ideal 69—5 Associator, nonassociative algebra 69—2 Asymmetric digraphs 35—2 see Asymptotic spectrum 47—8 Asymptotic stability, control theory 57—2 Asymptotic stability, linear differential-algebraic equations 55—14 Asymptotic stability, linear ordinary differential equations 55—10 Asymptotic stability, LTI systems 57—7 Asymptotics, matrix powers 25—8 to 25—9 ATLAST M-file collection 71—20 Attractor-repeller decompositions 56—7 Augmented matrices, Bezout domains 23—9 Augmented matrices, systems of linear equations 1—9 1—11 Augmented systems, least squares solution 39—4 Autocorrelation matrix 64—5 Autocorrelation sequence 64—4 Automatic, Mathematica software, fundamentals 73—27 Automatic, Mathematica software, singular values 73—17 Automorphism, Lie algebras 70—1 Automorphism, ring, linear preservers 22—7 Autonomy, control theory 57—2 Backward errors, analysis 37—20 Backward errors, numerical stability and instability 37—18 37—20 Backward errors, one-sided Jacobi SVD algorithm 46—2 Backward stability, numerical stability and instability 37—18 Backward stability, numerical stability and instability, one-sided Jacobi SVD algorithm 46—2 BackwardsSubstitute, Maple software 72—9 Bad columns 50—8 Bad rows 50—8 Badly-conditioned data 37—7 Bai, Zhaojun 75—1 to 75—23 Bailey, D. 47—5
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