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Hogben L. — Handbook of Linear Algebra
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Íàçâàíèå: Handbook of Linear Algebra
Àâòîð: 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.
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Ãîä èçäàíèÿ: 2006
Êîëè÷åñòâî ñòðàíèö: 1400
Äîáàâëåíà â êàòàëîã: 30.06.2008
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Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
Ïðåäìåòíûé óêàçàòåëü
Partitioned matrices, random vectors 52—3
Partitioned matrices, Schur complements 10—6 to 10—8
Partitioned matrices, submatrices 10—1 to 10—3
Partitioned matrices, submatrices and block matrices 10—1
Partly decomposable 27—3
Pascal matrices, factorizations 21—6
Pascal matrices, totally positive and negative matrices 21—4
Passage class 54—5
Path cover number 34—4
Path of length 28—1 28—2
Path, digraphs 29—2
Path, modeling and analyzing fill 40—10
Path, sign-pattern matrices 33—2
Path-connection P—5
Pattern block triangular form 35—2
Patterns 27—1 see
Payoff matrix 50—18
Peak characteristics 26—9
peaks function, Matlab software 71—17
PEIEPs (prescribed entries inverse eigenvalue problems) 20—1 to 20—3
PEIPs see «Affine parameterized IEPs (PIEPs)»
Pencils, matrix, generalized eigenvalue problem 43—2
Pencils, matrix, linear differential-algebraic equations 55—7
Pencils, matrix, matrices over integral domains 23—9 to 23—10
Pendant path 34—2
Penrose conditions 5—12
Perfect code 61—2
Perfect elimination ordering, bipartite graphs 30—4
Perfect elimination ordering, reordering effect 40—14
Perfect matching 30—2
Perfectly well determined, high relative accuracy 46—8
Period, complex sign and ray patterns 33—14
Period, Fourier analysis 58—2
Period, imprimitive matrices 29—10
Period, irreducible matrices 9—3
Period, linear dynamical systems 56—5
Period, reducible matrices 9—7
Period, Simon’s problem 62—13
Periodic characteristics, Fourier analysis 58—2
Periodic characteristics, irreducible classes 54—5
Periodic characteristics, linear dynamical systems 56—5
Periodic linear differential equations 56—12 to 56—14
Peripheral eigenvalues 26—6
Peripheral spectrum, cone invariant departure, matrices 26—5 to 26—7
Peripheral spectrum, Perron — Schaefer condition 26—6
perm, Mathematica software 73—19
permanent, Mathematica software 73—12
Permanental dominance conjecture 31—13
Permanents, -matrices 31—8
Permanents, binary matrices 31—5 to 31—7
Permanents, determinant connections 31—12 to 31—13
Permanents, doubly stochastic matrices 31—3 to 31—4
Permanents, evaluation 31—11 to 31—12
Permanents, fundamentals 31—1 to 31—3
Permanents, matrices over 31—8 to 31—9
Permanents, max-plus algebra 25—9 to 25—10
Permanents, nonnegative matrices 31—7
Permanents, rook polynomials 31—10 to 31—11
Permanents, subpermanents 31—9 to 31—10
permMatr, Mathematica software 73—19
Permutation invariants, absolute norm 17—5
Permutation invariants, vector norms 37—2
Permutation matrix, fundamentals 1—6
Permutation matrix, Gauss elimination 38—7
Permutation matrix, matrices 1—4
Permutation matrix, systems oflinear equations 1—13
Permutations, eigenvalue problems 15—2
Permutations, equivalence 31—1
Permutations, fundamentals P—5
Permutations, pattern 33—2
Permutations, representation 68—3
Permutations, restricted positions 31—6
Permutations, similarity 27—5 33—2
Perpendicular bisectors 65—4
Perpendicular hyperplanes 66—2
Perron branch 36—5
Perron component 36—10
Perron spaces, Collatz — Wielandt sets 26—4
Perron spaces, K-reducible matrices 26—10
Perron value, convergence properties 9—9 to 9—10
Perron value, irreducible matrices 9—4 to 9—5
Perron value, nonnegative and stochastic matrices 9—2
Perron value, nonzero spectra 20—7
Perron value, reducible matrices 9—8 to 9—10
Perron — Frobenius theorem, cone invariant Perron — Frobenius theorem, departure, matrices 26—1 to 26—3
Perron — Frobenius theorem, elementary analytic results 26—12
Perron — Frobenius theorem, irreducible matrices 9—4 29—6
Perron — Frobenius-type results 9—10
Perron — Schaefer condition 26—5 to 26—7
Perron’s theorem 9—3
Persistently exciting of order 64—12
Personalization vector 63—11
Pertinent pages, Web search 63—9
Perturbation theory, matrices, eigenvalue problems 15—1 to 15—6 15—9 15—13
Perturbation theory, matrices, polar decomposition 15—7 to 15—9
Perturbation theory, matrices, relative distances 15—13 to 15—16
Perturbation theory, matrices, singular value problems 15—6 to 15—7 15—12 15—15
Perturbations 38—2 to 38—5
Perturbed linear system 38—2
Petersen graphs, adjacency matrices 28—7
Petersen graphs, embedding 28—5
Petersen graphs, graph parameters 28—10
Petersen graphs, Laplacian 28—9
Petersen graphs, nonsquare case 32—11
Petrie matrix 30—4 30—5 30—7
Petrov — Galerkin projection, Arnoldi process 49—10
Petrov — Galerkin projection, eigenvalue computations 49—12
Petrov — Galerkin projection, Krylov subspaces 49—5
Petrov — Galerkin projection, large-scale matrixcomputations 49—2
Petrov — Galerkin projection, symmetric Lanczos process 49—7
Pfaffian properties 12—5
Phase 2 geometric interpretation 50—13
Phillips regularization 39—9
Physical sciences applications 59—1 to 59—11
Pi function, Mathematica software 73—26
pi function, Matlab software 71—4
Pi theorem 47—8 47—9
Pick’s inequalities 14—2
PID (principal ideal domain) 23—2
Pierce decomposition 69—13
Pillai’s trace statistic 53—13
Pinching, inequalities 17—7
Pisarenko’s method 64—14
Pivot column 1—7
Pivot row 1—7
Pivot step 50—10
Pivoted QR factorization 39—11
Pivoting, elements, Jacobi method 42—17
Pivoting, elimination 1—7 38—7
Pivoting, Gauss — Jordan elimination 1—7
Pivoting, Jacobi method 42—17 42—18
Pivoting, linear programming 50—10 to 50—11
Pivoting, LU decomposition 38—10
Pivoting, positions 1—7
Pivoting, preconditioned Jacobi SVD algorithm 46—5
Pivoting, reordering effect 40—18
Planar graphs 28—4
Planck’s constant 59—6
Plane, affine spaces 65—2
planerot function, Matlab software 42—9
PLDU factorization 1—14 to 1—15
plot command, Matlab software 71—14
Plotkin bound 61—5
PLU factorization 1—13
Plus algebra 69—3
Plus, Mathematica software 73—27
PO (potentially orthogonality) 33—16
Poincare — Bendixson theorem 56—8
Poincare — Birkhoff — Witt theorem, Lie algebras 70—3
Poincare — Birkhoff — Witt theorem, Malcev algebras 69—17
Poincare — Birkhoff — Witt theorem, nonassociative algebra 69—3
Point spaces 66—1 to 66—5
Point-wise bounded 37—3
Point-wise similarity 24—1
Pointed cones 8—10
Points, affine spaces 65—2
Points, Euclidean point space 66—1
Points, projective spaces 65—6
Poisson’s equation, discrete theory 58—12
Poisson’s equation, Green’s functions 59—11
Polar cones 51—3
Polar decomposition, perturbation theory 15—7 to 15—9
Polar decomposition, singular values 17—1
Polar form, positive definite matrices 8—7
Polar form, singular values 17—1
PolarDecomposition, Mathematica software 73—19
Polarization formula 12—8
Polarization identity 5—3 13—11
Policy iteration algorithm 25—7
Polya matrix 21—11
Polyhedral cones 26—4
Polynomials, adjacency matrix 28—5
Polynomials, certain integral domains 23—1
Polynomials, eigenvalues and eigenvectors 4—6 4—8
Polynomials, interpolation 11—2
Polynomials, linear code classes 61—7
Polynomials, numerical hull 41—16
Polynomials, restarting 44—5 to 44—6
Polynomials, span and linear independence 2—2
Polynomials, stability 19—3
Polynomials, vector spaces 1—3
Polynomials, zeros 37—8
PolynomialTools, Maple software 72—20 72—21
Population 52—2
Population canonical correlations and variates 53—7
Population principal component 53—5
Positionally symmetric partial matrix 35—2
Positive definite Jacobi EVD 46—11
Positive definite matrices (PSD) see «Completely positive matrices»
Positive definite matrices (PSD), completion problems 35—8 to 35—9
Positive definite matrices (PSD), fundamentals 8—6 to 8—12
Positive definite matrices (PSD), high relative accuracy 46—10 to 46—14
Positive definite matrices (PSD), inner product spaces 5—2
Positive definite matrices (PSD), symmetric factorizations 38—15
Positive definite properties, Hermitian forms 12—8
Positive definite properties, matrix norms 37—4
Positive definite properties, symmetric bilinear forms 12—3
Positive definite properties, vector norms 37—2
Positive definite properties, vector seminorms 37—3
Positive properties see «Nonnegatives»
Positive properties, eigenvectors 9—11
Positive properties, Fiedler vectors 36—7
Positive properties, generalized eigenvectors 9—11
Positive properties, half-life 13—24
Positive properties, matrix mapping 18—11
Positive properties, orientation 13—24
Positive properties, P-matrices 35—17 to 35—18
Positive properties, Perron — Frobenius theorem 26—2
Positive properties, recurrent state 54—7 to 54—9
Positive properties, root, semisimple and simple algebras 70—4
Positive properties, stability 19—3 26—13
Positive properties, stable matrices 9—17
Positive properties, vector seminorms 37—3
Positive semidefinite properties, completion problems 35—8 to 35—9
Positive semidefinite properties, Hermitian forms 12—8
Positive semidefinite properties, matrix completion problems 35—8
Positive semidefinite properties, positive definite matrices 8—6
Positive semidefinite properties, semidefinite programming 51—3
Positive semidefinite properties, symmetric bilinear forms 12—3
Positive/null recurrent state 54—7 to 54—9
Potent square sign or ray patterns 33—14
Potential energy, Lagrangian mechanics 59—5
Potential energy, oscillation modes 59—2
Potential energy, protein motion modes 60—9
Potential matrix 54—7 to 54—9
Potential stability 33—7
Potentially orthogonality (PO) 33—16
Potentials, duality 50—17
Powell-Reid’s complete pivoting 46—5 46—7
Power associative algebras, general properties 69—5
Power associative algebras, nonassociative algebra 69—14 to 69—16
Power, algorithm 25—7
Power, convergence properties 9—4 9—9
Power, irreducible matrices 9—4
Power, matrices 1—12
Power, method 42—2
Power, mth, matrices 1—12
Power, reducible matrices 9—9
Power, sign-pattern matrices 33—15 to 33—16
Power, symmetric and Grassmann tensors 13—12
Power, tensor products 13—3
Precision, Mathematica software 73—17
Precisions, ARPACK subroutine package 76—3 to 76—4
Precisions, floating point numbers 37—12
Precisions, vector space method 63—2
Preconditioned conjugate gradient (PCG) algorithm 41—13
Preconditioned Jacobi SVD algorithm 46—5 to 46—7
Preconditioners, iterative solution methods, algorithms 41—12 to 41—14
Preconditioners, iterative solution methods, fundamentals 41—11 to 41—12
Preconditioners, iterative solution methods, Krylov subspaces 41—2 to 41—4
Preconditioning, algorithms 41—12 to 41—14
Preconditioning, coefficient matrix 49—4
Preconditioning, iteration matrices 41—3
Preconditioning, Jacobi SVD algorithm 46—5 to 46—7
Preconditioning, Krylov subspaces and preconditioners 41—3
Preconditioning, sparse matrix factorizations 49—4
Predicable random signals 64—7
Prediction error 64—7
Prediction error filter 64—7
prefixes 74—2
Prepend, Mathematica software, matrices manipulation 73—13
Prepend, Mathematica software, vectors 73—3
Prescribed entries inverse eigenvalue problems (PEIEPs) 20—1 to 20—3
Prescribed-line-sum scalings 9—21
Preservation see «Linear preserver problems»
Preservation, bilinear forms 12—2
Preservation, linear dynamical systems 56—5
Preservation, Lyapunov diagonal stability 19—9
Preservation, multiplicative D-stability 19—5
Preservation, sesquilinear forms 12—6
Primal-dual interior point algorithm 51—8 to 51—9
Primary decomposition 6—9
Primary Decomposition Theorem, eigenvectors 6—2
Primary Decomposition Theorem, rational canonical form 6—10
Primary factors 6—9
Primary matrix function 11—2
Prime elements 23—2
Primitive Bose — Chadhuri — Hocquenghem (BCH) code 61—8
Primitive properties, certain integral domains 23—2
Primitive properties, digraphs and matrices 29—8 to 29—9
Primitive properties, elements 69—18
Primitive properties, gates 62—7
Principal angles 17—14 17—15
Principal Axes Theorem 7—5 to 7—6
Principal character 68—5
Principal component 26—12
Principal component analysis 53—5 to 53—6
Principal eigenprojection 26—12
Principal ideal domain (PID) 23—2
Principal ideals 23—2
Principal logarithm 11—6
Principal minors, determinants 4—3
Principal minors, stability 19—3
Principal parts 24—1
Principal square root 11—5
Principal submatrix, fundamentals 1—6
Principal submatrix, matrices 1—4
Principal submatrix, reducible matrices 9—7
Principal submatrix, submatrices and block matrices 10—1
Principal vectors 17—14
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