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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
Chordal symmetric Hamiltonian, minimally 35—15 Chromatic index 27—10 Chromatic number 28—9 Chu, Ka Lok 53—14 circul function, Matlab software 71—6 Circulant matrices, Maple software 72—18 Circulant matrices, nonnegative inverse eigenvalue problems 20—5 Circulant matrices, structured matrices 48—2 Circumcenter 66—8 Circumscribed hypersphere 66—8 Class functions, orthogonality relations 68—6 Classical Gram-Schmidt (CGS) scheme 44—3 to 44—4 Classical groups 67—5 to 67—7 Classical Turing machine 62—2 Classification Theorem 24—9 24—11 Classification, states 54—7 to 54—9 Classifications I and II 24—7 to 24—11 Clifford algebra 69—13 Clifford’s theorem, characters 68—9 Clifford’s theorem, matrix groups 67—2 Cline, Alan Kaylor 45—1 to 45—12 Clique number 28—9 Clique, graph parameters 28—9 Clique, graphs 35—2 Close cones 8—10 Closed ball of radius 61—2 Closed halfspace 66—2 Closed subset 50—13 Closed under matrix direct sums 35—2 Closed under permutation similarity 35—2 Closed under taking principal submatrices 35—2 Closed walk 54—5 Closed-loop ODE 57—2 Closed-loop system 57—13 Closure under addition 1—2 Closure under scalar multiplication 1—2 Co-cover 27—2 Co-index 9—7 Cockades 30—4 Cocktail party graph 28—4 Coclique 28—9 Codewords 61—1 Codimension 66—2 Coding theory, convolutional codes 61—11 to 61—13 Coding theory, distance bounds 61—5 to 61—6 Coding theory, fundamentals 61—1 to 61—2 Coding theory, linear block codes 61—3 to 61—4 Coding theory, linear code classes 61—6 to 61—11 Coding theory, main linear coding problem 61—5 to 61—6 Codomain 3—1 Coefficient matrices, Bezout domains 23—9 Coefficient matrices, linear differential equations 55—1 Coefficients, determination 52—8 Coefficients, multiple determination 52—8 Coefficients, systems of linear equations 1—9 Cofactors, determinants 4—1 Cogame utility, ATLAST 71—20 71—22 Colin de Verdiere parameter 28—9 28—10 Collatz-Wielandt sets, cone invariant departure, matrices 26—3 to 26—5 Collatz-Wielandt sets, irreducible matrices 9—5 Collineation, projective spaces 65—7 Colonius, Fritz 56—1 to 56—21 Color class 28—9 ColorFunction, Mathematica software 73—27 colormap command, Matlab software 71—15 colspace command, Matlab software 71—17 Column-stochastic matrices 9—15 Columns, equivalence 23—5 Columns, feasibility 50—14 Columns, indices 23—9 Columns, linear independence, span, and bases 2—6 Columns, matrices 1—3 Columns, pivoting 46—5 Columns, rank 25—13 Columns, sign solvability 33—5 Columns, signing, balanced 33—5 Columns, sum vector 27—7 Columns, vectors 1—3 Combinatorial matrix theory, algebraic connectivity 36—1 to 36—11 Combinatorial matrix theory, bipartite graphs and matrices 30—1 to 30—10 Combinatorial matrix theory, classes of (0, 1)-matrices 27—7 to 27—10 Combinatorial matrix theory, completion problems 35—1 to 35—20 Combinatorial matrix theory, convex polytopes 27—10 to 27—12 Combinatorial matrix theory, D-optimal matrices 32—1 to 32—12 Combinatorial matrix theory, digraphs 29—1 to 29—13 Combinatorial matrix theory, doubly stochastic matrices 27—10 to 27—12 Combinatorial matrix theory, fundamentals 27—1 to 27—12 Combinatorial matrix theory, graphs 28—1 to 28—12 Combinatorial matrix theory, monotone class 27—7 to 27—8 Combinatorial matrix theory, multiplicity lists 33—1 to 33—17 Combinatorial matrix theory, permanents 31—1 to 31—13 Combinatorial matrix theory, sign-pattern matrices 33—1 to 33—17 Combinatorial matrix theory, square matrices 27—3 to 27—6 Combinatorial matrix theory, strong combinatorial invariants 27—3 to 27—5 Combinatorial matrix theory, structure and invariants 27—1 to 27—3 Combinatorial matrix theory, tournament matrices 27—8 to 27—10 Combinatorial matrix theory, weak combinatorial invariants 27—5 to 27—6 Combinatorial orthogonality 33—16 Combinatorial problems 47—10 Combinatorial symmetric partial matrix 35—2 Combinatorial symmetric sign pattern matrices 33—9 Communication, irreducible classes 54—5 Communication, irreducible matrices 29—6 Communication, nonnegative and stochastic matrices 9—2 Commutative algebras 69—2 Commutative ring, certain integral domains 23—1 Commutative ring, permanents 31—1 Commutativity and Jordan identity 69—12 Commutativty axiom 1—1 Commutators, nonassociative algebra 69—2 Commutators, Schrodinger’s equation 59—7 Commute, matrices 1—4 Commute, vector spaces 3—2 Companion matrices, eigenvalues and eigenvectors 4—6 Companion matrices, rational canonical forms 6—8 CompanionMatrix, Maple software 72—17 Comparison matrices 19—9 Compatibility 33—2 Complement, binary matrices 31—5 Complement, fundamentals P—1 Complement, graphs 28—2 Complementary parameters 64—8 Complementary projections 3—6 Complementary slackness, duality 50—14 Complementary slackness, duality and optimality conditions 51—6 Complementary slackness, max-plus eigenproblem 25—7 Complete bipartite graphs 28—2 30—1 see Complete flag 56—9 Complete graphs 28—2 see Complete min-plus semiring 25—1 Complete orthogonal decomposition 39—11 Complete orthogonal set 5—3 Complete pivoting 38—10 see Complete reducibility, matrix group 67—1 Complete reducibility, modules 70—7 Complete reducibility, square matrices, weak combinatorial invariants 27—5 Completed max-plus semiring 25—1 Completely positive matrices, completion problems 35—10 to 35—11 Completely positive matrices, nonnegative factorization 9—22 Completion problems, matrices, completely positive matrices 35—10 to 35—11 Completion problems, matrices, copositive matrices 35—11 to 35—12 Completion problems, matrices, doubly nonnegative matrices 35—10 to 35—11 Completion problems, matrices, entry sign symmetric P-, 35—19 to 35—20 Completion problems, matrices, entry weakly sign symmetric P-, 35—19 to 35—20 Completion problems, matrices, Euclidean distance matrices 35—9 to 35—10 Completion problems, matrices, fundamentals 35—1 to 35—8 Completion problems, matrices, inverse M-matrices 35—14 to 35—15 Completion problems, matrices, M- and 35—12 to 35—13 Completion problems, matrices, nonnegative P-, 35—17 to 35—18 Completion problems, matrices, P-, 35—15 to 35—17 Completion problems, matrices, positive definite matrices 35—8 to 35—9 Completion problems, matrices, positive P-matrices 35—17 to 35—18 Completion problems, matrices, positive semidefinite matrices 35—8 to 35—9 Completion problems, matrices, strictly copositive matrices 35—11 to 35—12 Completion property 35—2 Complex conjugate 68—5 Complex elements, Maple software 72—7 Complex numbers, fundamentals P—1 to P—2 Complex numbers, nonassociative algebra 69—4 Complex polynomial 19—3 Complex sign patterns 33—14 to 33—15 Complexity, convolutional codes 61—12 Component backward stable 38—6 Component-wise perturbation theory 39—7 Component-wise relative backward errors, linear system 38—2 Component-wise relative distance 46—10 Composite cycle 33—2 Composition algebras 69—8 to 69—10 Composition, symmetric and Grassmann tensors 13—13 Compound matrix 4—3 Compressed column storage (CCS) scheme 40—3 Compressed row storage (CRS) scheme 40—4 Computational linear algebra, fast matrix multiplication 47—1 to 47—10 Computational linear algebra, large-scale matrix computations 49—1 to 49—15 Computational linear algebra, structured matrix computations 48—1 to 48—9 Computational methods 69—20 to 69—25 Computational modes 76—8 to 76—9 Computational software, freeware 77—1 to 77—3 Computational software, Maple 72—1 to 72—21 Computational software, Mathematica 73—1 to 73—27 Computational software, Matlab 71—1 to 71—22 Computational software, subroutine packages, ARPACK 76—1 to 76—10 Computational software, subroutine packages, BLAS 74—1 to 74—7 Computational software, subroutine packages, EIGS 76—1 to 76—10 Computational software, subroutine packages, LAPACK 75—1 to 75—23 Computations, large-scale matrices, Arnoldi process 49—10 to 49—11 Computations, large-scale matrices, dimension reduction 49—14 to 49—15 Computations, large-scale matrices, eigenvalue computations 49—12 Computations, large-scale matrices, fundamentals 49—1 to 49—2 Computations, large-scale matrices, Krylov subspaces 49—5 to 49—6 Computations, large-scale matrices, linear dynamical systems 49—14 to 49—15 Computations, large-scale matrices, linear systems, equations 49—12 to 49—14 Computations, large-scale matrices, nonsymmetric Lanczos process 49—8 to 49—10 Computations, large-scale matrices, sparse matrix factorizations 49—2 to 49—5 Computations, large-scale matrices, symmetric Lanczos process 49—6 to 49—7 Computations, pseudospectra 16—11 to 16—12 Computations, singular value decomposition 45—1 to 45—12 Computations, structured matrices, direct Toeplitz solvers 48—4 to 48—5 Computations, structured matrices, fundamentals 48—1 to 48—4 Computations, structured matrices, iterative Toeplitz solvers 48—5 Computations, structured matrices, linear systems 48—5 to 48—8 Computations, structured matrices, total least squares problems 48—8 to 48—9 Computer science applications, coding theory 61—1 to 61—13 Computer science applications, information retrieval 63—1 to 63—14 Computer science applications, quantum computation 62—1 to 62—19 Computer science applications, signal processing 64—1 to 64—18 Computer science applications, Web searches 63—1 to 63—14 Concentration, metabolites 60—10 Conceptual PageRank 63—11 see cond, Mathematica software 73—18 Condensation digraph 29—7 Condensation method 4—4 Condition numbers, linear system perturbations 38—2 Condition numbers, polar decomposition 15—8 Condition numbers, sensitivity 39—7 Conditioning of eigenvalues, Maple software 72—15 Conditioning, condition numbers 37—7 to 37—9 Conditioning, linear systems 37—9 to 37—11 ConditionNumber, Maple software 72—9 Conductance 28—9 Conductivity 66—13 Cone invariant departure, matrices, Collatz-Wielandt sets 26—3 to 26—5 Cone invariant departure, matrices, core 26—5 to 26—7 Cone invariant departure, matrices, distinguished eigenvalues 26—3 to 26—5 Cone invariant departure, matrices, elementary analytic results 26—12 to 26—13 Cone invariant departure, matrices, fundamentals 26—1 Cone invariant departure, matrices, K-reducible matrices 26—8 to 26—10 Cone invariant departure, matrices, linear equations over cones 26—11 to 26—12 Cone invariant departure, matrices, peripheral spectrum 26—5 to 26—7 Cone invariant departure, matrices, Perron-Frobenius theorem 26—1 to 26—3 Cone invariant departure, matrices, Perron-Schaefer condition 26—5 to 26—7 Cone invariant departure, matrices, spectral theory 26—8 to 26—10 Cone invariant departure, matrices, splitting theorems 26—13 to 26—14 Cone invariant departure, matrices, stability 26—13 to 26—14 Cones, Perron-Frobenius theorem 26—1 to 26—3 Cones, positive definite matrices 8—10 Cones, programming 51—2 Cones, reducible matrices 26—8 Conformal and conformable partitions 10—1 Conformal partitions 10—1 Congruence, bilinear forms 12—2 Congruence, Hermitian and positive definite matrices 8—5 to 8—6 Congruence, Hermitian forms 12—8 Congruence, linear inequalities and projections 25—10 Congruence, sesquilinear forms 12—6 Conjugacy 56—5 Conjugate character 68—9 Conjugate Gradient (CG) algorithm, convergence rates 41—14 to 41—15 Conjugate Gradient (CG) algorithm, Krylov space methods 41—4 41—6 Conjugate Gradient Squared (CGS) algorithm 41—8 Conjugate partition P—2 Conjugates, linear dynamical systems 56—5 ConjugateTranspose, Mathematica software, fundamentals 73—27 ConjugateTranspose, Mathematica software, matrix algebra 73—9 73—11 ConjugateTranspose, Mathematica software, singular values 73—17 73—18 Connected properties and components, digraphs 29—2 Connected properties and components, graphs 28—1 28—2 Consecutive ones property 30—4 Consistency, least squares solution 39—1 Consistency, linear differential equations 55—2 Consistency, linear statistical models 52—8 Consistency, matrix norms 37—4 Consistency, systems of linear equations 1—9 Consistent sign pattern matrices 33—9 Constant Boolean function, Deutsch-Jozsa problem 62—9 Constant Boolean function, Deutsch’s problem 62—8 Constant coefficients, differential equations 55—1 to 55—5 Constant coefficients, linear differential equations 55—1 Constant term 1—9 Constant vector 1—9 Constituents, characters 68—5 ConstrainedMax, Mathematica software 73—27 ConstrainedMin, Mathematica software 73—27 Constraint length 61—12 Constraint qualification, semidefinite programming 51—7 Constraint qualification, strong duality 51—7 Contact matrix 60—9 Containment gap 44—9 Content index, Web search 63—9 Continuation character backslash, Maple software 72—2 Continuous dynamical systems 56—5 Continuous invariants 24—11 Continuous real-valued functions 2—2 contour command, Matlab software 71—15 Contour integration 11—10 Contraction matrices 18—9 Contractions, graphs 28—4 Contragredient 68—3 Control design, LTI systems 57—13 to 57—17 Control system 57—2 Control theory, analysis, LTI systems 57—7 to 57—10 Control theory, control design, LTI systems 57—13 to 57—17 Control theory, frequency-domain analysis 57—5 to 57—6 Control theory, fundamentals 57—1 to 57—5 Control theory, LTI systems 57—7 to 57—10 57—13 Control theory, matrix equations 57—10 to 57—11 Control theory, state estimation 57—11 to 57—13 Control vector 57—2 Controllability Hessenberg form 57—9 Controllability matrix 57—7
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