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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

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Год издания: 2006

Количество страниц: 1400

Добавлена в каталог: 30.06.2008

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Предметный указатель

Nondefective matrices      4—6
Nondegenerate properties, bilinear forms      12—2
Nondegenerate properties, sesquilinear forms      12—6
Nonderogatory matrices      4—6
Nondifferentiation      18—3
Nonempty sets, row and column indices      1—4
Nonhomogenous products      9—22
Nonlinear preservers      22—7 to 22—8
Nonnegative IEPs (NIEPs), fundamentals      20—5
Nonnegative IEPs (NIEPs), merging results      20—8
Nonnegative IEPs (NIEPs), nonzero spectra      20—7 to 20—8
Nonnegative IEPs (NIEPs), spectra      20—6 to 20—7
Nonnegative IEPs (NIEPs), sufficient conditions      20—8 to 20—10
Nonnegatives, constraints      50—3
Nonnegatives, factorization      9—22
Nonnegatives, fundamentals      9—1
Nonnegatives, integer rank      30—8
Nonnegatives, matrices, fundamentals      9—1 to 9—2
Nonnegatives, matrices, inequalities      17—11
Nonnegatives, matrices, inverse eigenvalue problem      9—22
Nonnegatives, matrices, irreducible matrices      9—2 to 9—7
Nonnegatives, matrices, max algebra      9—23
Nonnegatives, matrices, nonhomogenous products      9—22
Nonnegatives, matrices, nonnegative factorization      9—22
Nonnegatives, matrices, P-, $P_{0, 1}-$ and $P_{0}$ -matrices, completion problems      35—17 to 35—18
Nonnegatives, matrices, permanents      31—7
Nonnegatives, matrices, Perron — Frobenius theorem      26—2
Nonnegatives, matrices, product form      9—23
Nonnegatives, matrices, reducible matrices      9—7 to 9—15
Nonnegatives, matrices, scaling      9—20 to 9—23
Nonnegatives, matrices, sets      9—23
Nonnegatives, matrix factorization      63—5 to 63—8
Nonnegatives, sign pattern matrices      33—12
Nonnegatives, stable matrices      9—17
Nonnegatives, vectors      26—2
Nonnormality constant      44—10
Nonprimary matrix function      11—2
Nonrandom matrices      52—3
Nonrandom vectors      52—3
Nonregular matrices      32—7 to 32—9
Nonscalar multiplications, approximation algorithms      47—6
Nonscalar multiplications, fast algorithms      47—2
Nonseparability      35—2
Nonsingular properties, distribution      53—8
Nonsingular properties, fundamentals      2—9 to 2—10
Nonsingular properties, isomorphism      3—7 to 3—8
Nonsingular properties, matrices      1—12
Nonsingular properties, multivariate normal distribution      53—3
Nonsquare case      32—2 to 32—12
Nonsymmetric eigenproblems      75—17 to 75—20
Nonsymmetric eigenvalue problems      75—11 to 75—13
Nonsymmetric Lanczos process, Arnoldi process      49—10
Nonsymmetric Lanczos process, large-scale matrixcomputations      49—8 to 49—10
Nonsymmetric Lanczos process, linear dynamical systems      49—15
Nonsymmetric problems, ARPACK      76—8
Nonzero spectra      20—7 to 20—8
norm command, Matlab software      71—17
Norm estimation      18—9 to 18—10
Norm, Maple software      72—3 72—5
Norm, Mathematica software, fundamentals      73—26 73—27
Norm, Mathematica software, matrix algebra      73—10 73—11
Norm, Mathematica software, vectors      73—3 73—5
Normal equations, least squares problems      5—14
Normal equations, linear statistical models      52—8
Normal vector, Euclidean point space      66—2
Normal, Mathematica software      73—6 73—8
Normalization      23—5
Normalized properties, floating point numbers      37—11
Normalized properties, immanant      31—13
Normalized properties, matrices      25—6
Normalized properties, scaling nonnegative matrices      9—20
Norms, matrices      37—4 to 37—6
Not invertible      1—12 see
Notation index      N—1 to N—9
Notebooks, Mathematica software      73—1
Nth-derived algebra      70—3
null command, Matlab software      71—8 71—17
Null graphs      28—2
Null recurrent state      54—7 to 54—9
Null spaces, dimension theorem      2—6 to 2—9
Null spaces, kernel and range      3—5
Null spaces, linear independence, span, and bases      2—6
Null spaces, matrix range      2—6 to 2—9
Null spaces, rank      2—6 to 2—9
Nullity, linear independence, span, and bases      2—6
Nullity, matrix equalities and inequalities      14—12 to 14—15
NullSpace, Maple software, matrix factoring      72—9
NullSpace, Maple software, modular arithmetic      72—14 to 72—15
NullSpace, Mathematica software, fundamentals      73—27
NullSpace, Mathematica software, matrix algebra      73—10 73—12
Nullspaces      39—4
Numerical linear algebra, Maple software      72—13 to 72—15
Numerical linear algebra, support routines      77—1
Numerical methods, affine parameterized IEPs      20—11 to 20—12
Numerical methods, fast matrix multiplication      47—1 to 47—10
Numerical methods, high relative accuracy computation      46—1 to 46—16
Numerical methods, implicitly restarted Arnoldi method      44—1 to 44—12
Numerical methods, iterative solution methods      41—1 to 41—17
Numerical methods, large-scale matrixcomputations      49—1 to 49—15
Numerical methods, linear systems, direct solutions      38—1 to 38—17
Numerical methods, linear systems, efficiency      37—1 to 37—21
Numerical methods, linear systems, error analysis      37—1 to 37—21
Numerical methods, linear systems, factorizations      38—1 to 38—17
Numerical methods, linear systems, least squares solutions      39—1 to 39—12
Numerical methods, linear systems, matrix norms      37—1 to 37—21
Numerical methods, linear systems, sparse matrix methods      40—1 to 40—18
Numerical methods, linear systems, stability      37—1 to 37—21
Numerical methods, linear systems, vector norms      37—1 to 37—21
Numerical methods, Markov chains      54—12 to 54—14
Numerical methods, singular value decomposition      45—1 to 45—12
Numerical methods, stability and instability      37—18 to 37—21
Numerical methods, structured matrix computations      48—1 to 48—9
Numerical methods, symmetric matrix techniques      42—1 to 42—22
Numerical methods, unsymmetric matrix techniques      43—1 to 43—11
Numerical orthogonality      46—2
Numerical radius      18—1
Numerical range, boundary points      18—3 to 18—4
Numerical range, dilations      18—9 to 18—10
Numerical range, examples      18—1 to 18—3
Numerical range, fundamentals      18—1
Numerical range, location      18—4 to 18—6
Numerical range, matrix mappings      18—11
Numerical range, matrix products      18—8 to 18—9
Numerical range, norm estimation      18—9 to 18—10
Numerical range, properties      18—1 to 18—3
Numerical range, radius      18—6 to 18—8
Numerical range, special boundary points      18—3 to 18—4
Numerical range, spectrum      18—3 to 18—4
Numerical range, unitary similarity      7—2
Numerical rank      39—11
Numerical stability and instability, error analysis      37—18 to 37—21
Numerical stability and instability, Strassen’s algorithm      47—4
Numerically orthogonal matrices      46—2
numnull command, Matlab software      71—13
O and o      P—5
Objective function      50—1
Oblique Petrov — Galerkin projection, eigenvalue Oblique Petrov — Galerkin projection, computations      49—12
Oblique Petrov — Galerkin projection, large-scale matrix computations      49—2
Observability Hessenberg form      57—9
Observability Kalman decomposition      57—7
Observability matrix      57—7
Observableness, control theory      57—2
Observer equation      57—2
Octonions, generalized      69—4
Odd cycle      33—2
Oettli — Prager theorem      38—3
Off-diagonal entry      1—4
Off-norm, Jacobi method      42—17
One(1)-chordal graphs      35—2
One(1)-norm      37—2

One-bit quantum gate      62—2
One-dimensional harmonic oscillator      59—8
One-sided Jacobi SVD algorithm, high relative accuracy      46—2 to 46—5
One-sided Jacobi SVD algorithm, positive definite matrices      46—11
One-sided Jacobi SVD algorithm, preconditioned Jacobi SVD algorithm      46—6
One-sided Jacobi SVD algorithm, singular value decomposition      45—5
One-sided Jacobi SVD algorithm, symmetric indefinite matrices      46—15
One-to-one, kernel and range      3—5
Onto, kernel and range      3—5
Open halfspaces      66—2
Open sector      33—14
Operations and functions, Maple software      72—3 72—5
Operator norms, matrix norms      37—4
Operator norms, unitary similarity      7—2
Optimal control problem      57—14
Optimal estimation problem      57—12
Optimal Krylov space methods      41—4 to 41—11
Optimal pivoting strategy      42—17
Optimal solution      50—1
Optimal value      50—1
Optimality conditions      51—5 to 51—7
Optimality theorem      51—6
Optimization, linear programming      50—1 50—1
Optimization, matrix games      50—18
Optimization, semidefinite programming      51—1 to 51—11
Optimization, standard row tableaux      50—8
Orbit, linear dynamical systems      56—5
Orbit, simultaneous similarity      24—8
Order predictable signals      64—7
Order sequence      58—8
Order, control theory      57—2
Order, graphs      28—1
Order, reducible matrices      26—9
Ordinary least squares estimator      52—8
Ordinary least squares solution      52—8
Orientation      13—24 to 13—26
Orientation preservation      56—5
Oriented incidence matrix      28—7
orth command, Matlab software      71—17
Orthogonal Petrov — Galerkin projection, Arnoldi process      49—10
Orthogonal Petrov — Galerkin projection, large-scale matrix computations      49—2
Orthogonal Petrov — Galerkin projection, symmetric Lanczos process      49—7
Orthogonal properties, classical groups      67—5
Orthogonal properties, complement      5—3
Orthogonal properties, congruence      25—10
Orthogonal properties, Euclidean point space      66—2
Orthogonal properties, Euclidean spaces      65—4
Orthogonal properties, fundamentals      5—3 to 5—5
Orthogonal properties, general properties      69—5
Orthogonal properties, least squares solutions      39—5 to 39—6
Orthogonal properties, linear inequalities and projections      25—10
Orthogonal properties, projection      5—6 to 5—8
Orthogonal properties, rank revealing decomposition      39—11
Orthogonal properties, sign-pattern matrices      33—16 to 33—17
Orthogonal properties, symmetric bilinear forms      12—3
Orthogonal properties, symmetric indefinite matrices      46—14
Orthogonal properties, symmetric matrix eigenvalue techniques      42—2
Orthogonal properties, unitary similarity      7—1
Orthogonality relations      68—6 to 68—8
Orthogonalization      38—13 to 38—15
Oscillation modes      59—2 to 59—5
Oscillatory matrices      21—2
Oseledets theorem      56—14 to 56—15
Ostrowski theorem, eigenvalue problems      15—13
Ostrowski theorem, spectrum localization      14—6 to 14—7
Outer normal, Euclidean simplexes      66—7
Outer, Mathematica software      73—2 73—3 73—4
Outerplanar graphs      28—4
OuterProductMatrix, Maple software      72—3
Outlets      66—13
Output Feedback      57—7 57—13
Output space      57—2
Output vector      57—2
Output, algorithms and efficiency      37—16
Output, LTI systems      57—14
Ovals of Cassini      14—6 to 14—7
Overall constraint length      61—12
Overflow, floating point numbers      37—12
P-, $P_{0, 1}-$ and $P_{0}$ -matrices, completion problems      35—15 to 35—17
P-, $P_{0, 1}-$ and $P_{0}$ -matrices, stability      19—3
p-Lie algebra      70—2
p-Norm      37—2
Packed format      74—2
Pade approximate      11—10 to 11—11 11—12
Pade iterations      11—12
Pade models, dimension reduction      49—14
Pade models, linear dynamical systems      49—15
PadRight, Mathematica software      73—13
Page repository      63—9
Page, Larry      54—4 63—9 63—10
PageRank, fundamentals      63—10
PageRank, information retrieval      63—10 to 63—14
PageRank, Markov chains      54—4 to 54—5
PageRank, vector      63—11
PageRank, Web search      63—9
Pairwise orthogonality      7—5
Paley — Wiener theorem      64—3 to 64—4
Pan, V.      47—7
Pappus’ theorem      65—8 65—9
Parabolic subgroup      67—4
Parabolic subgroup, BN structure      67—5
Parallel hyperplanes      66—2
Parallel vector subspace      65—2
Parallelepiped, Gram matrices      66—5
Parallelogram law, inner product spaces      5—3
Parallelogram, Gram matrices      66—5
Parameters, graphs      28—9 to 28—11
Parametric programming      50—17 to 50—18
Parametrization ofcorrelation matrices      8—8
Parity check, matrix      61—3
Parity check, polynomial      61—7
Parlett and Reinsch studies      43—3
Parlett’s recurrence      11—10 11—11
Parseval’s Inequality      5—4
Parter vertices      34—2 to 34—4
Parter — Wiener theorem, given multiplicities      34—9
Parter — Wiener theorem, multiplicities and Parter vertices      34—2
Parter — Wiener vertex      34—2
Partial $M_{0}$ -matrices      35—12 to 35—13
Partial completely positive matrices      35—10
Partial copositive matrices      35—11
Partial correlarandom vectors      52—4
Partial correlation coefficient, linear prediction      64—8
Partial correlation matrix      52—4
Partial covariance matrix      52—4
Partial differential equations      58—7
Partial doubly nonnegative matrices      35—10
Partial entry sign symmetric P-, $P_{0, 1}-$ and $P_{0}$ -matrices      35—19 to 35—20
Partial entry weakly sign symmetric P-, $P_{0, 1}-$ and $P_{0}$ -matrices      35—19 to 35—20
Partial Euclidean distance matrices      35—10
Partial inverse M-matrices      35—14
Partial M-matrices      35—12 to 35—13
Partial matrices      35—2
Partial matrix multiplication      47—8
Partial nonnegative P-, $P_{0, 1}-$ and -matrices      35—17 to 35—18
Partial order, checkerboard      21—9
Partial P-, $P_{0, 1}-$ and -matrices      35—15
Partial pivoting      40—18 see
Partial positive definite matrices      35—8
Partial positive P-matrices      35—17
Partial positive semidefinite matrices      35—8
Partial Schur decomposition      44—6 44—8
Partial semidefinite ordering, positive definite matrices      8—10
Partial semidefinite ordering, random vectors      52—4
Partial strictly copositive matrices      35—11
Partition, Mathematica software      73—14
Partitioned matrices, block diagonal matrices      10—4 to 10—6
Partitioned matrices, block matrices      10—1 to 10—3
Partitioned matrices, block triangular matrices      10—4 to 10—6
Partitioned matrices, Kronecker products      10—8 to 10—9

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