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Hogben L. — Handbook of Linear Algebra

Hogben L. — Handbook of Linear Algebra

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Название: Handbook of Linear Algebra

Автор: Hogben L.

Аннотация:

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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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 1400

Добавлена в каталог: 30.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

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, $(\pm 1)$ -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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