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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

Controlled-NOT gate, quantum computation      62—4
Controlled-NOT gate, universal quantum gates      62—8
Controller, LTI systems      57—13
Controlling random vectors      52—4
Convergence rates, CG      41—14 to 41—15
Convergence rates, GMRES      41—15 to 41—16
Convergence rates, MINRES      41—14 to 41—15
Convergence, implicitly restarted Arnoldi method      44—9 to 44—10
Convergence, nonnegative and stochastic matrices      9—2
Convergence, reducible matrices      9—8 9—11
Convergence, Toeplitz matrices      16—6
Convergent regular splitting      9—17
Convex hull      66—2
Convex linear combination      50—13
Convex polytopes      27—10 to 27—12
Convexity, affine spaces      65—2
Convexity, Euclidean point space      66—2
Convexity, fundamentals      P—2
Convexity, phase 2 geometric interpretation      50—13
Convexity, vector norms      37—3
Convexity, vector seminorms      37—4
Convolution identities, discrete theory      58—10
Convolution identities, Fourier analysis      58—5
Convolution, Fourier analysis      58—3
Convolution, signal processing      64—2
Convolutional codes      61—11 to 61—13
Coordinate matrix      60—2
Coordinate vectors      60—2
Coordinates, change of basis      2—10 to 2—12
Coordinates, Euclidean point space      66—1
Coordinates, NMR protein structure determination      60—2
Coordinatization theorem      69—13
Copositive matrices      35—11 to 35—12
Coppersmith and Winograd studies      47—9
Coprime elements      23—2
Core      26—5 to 26—7
Corless, Robert M.      72—1 to 72—21
Corner minor      21—7 see
Corrected seminormal equations      39—6
Correlation coefficient      52—3
Correlation matrix, positive definite matrices      8—6
Correlation matrix, random vectors      52—4
Correlation, random vectors      52—3
Correlations and variates      53—7 to 53—8
Cosine and sine      11—11
Cospectral graphs      28—5
costs, Mathematica software      73—24
Coupling time      25—9
Courant — Fischer inequalities      14—4
Courant — Fischer theorem, eigenvalues      14—4
Courant — Fischer theorem, Hermitian matrices      8—3
Covariance matrix, positive definite matrices      8—9
Covariance matrix, random vectors      52—3
Covariance, random vectors      52—3
Cover, combinatorial matrix theory      27—2
Cramer’s Rule      4—3 37—17
Craven and Csordas studies      21—11 to 21—12
Critical digraphs      25—6 25—7 see
Critical vertices      25—6
Cross correlation      64—4
Cross, Mathematica software      73—3 73—5
Cross-covariance matrix      52—4
Cross-positives      26—13
CrossProduct, Maple software      72—3
CRS (compressed row storage) scheme      40—4
Csordas, Craven and, studies      21—11 to 21—12
Cubics, Mathematica software      73—14 73—15
Cui, Feng      60—13
Cumulative distribution function      52—2
Cut lattice      30—2
Cut space      30—2
Cut vertices      36—3
Cuthill — McKee algorithm      40—16
Cycle conditions      35—9
Cycle of length      28—1 28—2
Cycle products, digraphs      29—4 to 29—6
Cycle-clique      35—14
Cycles of length      33—2
Cycles, digraphs      29—2
Cycles, Jacobi method      42—18
Cycles, matrices      48—2
Cycles, pattern      33—9
Cycles, simplex method      50—12
Cycles, time      25—8
Cyclic code      61—6
Cyclic normal form, digraphs      29—9 to 29—11
Cyclic normal form, imprimitive matrices      29—10
Cyclic simplexes      66—12
Cyclically real ray pattern      33—14
Cyclicity theorem      25—8
Cyclicity, matrix power asymptotics      25—8
D-optimal matrices, balanced matrices      32—12
D-optimal matrices, fundamentals      32—1
D-optimal matrices, nonregular matrices      32—7 to 32—9
D-optimal matrices, nonsquare case      32—2 to 32—12
D-optimal matrices, regular matrices      32—5 to 32—7
D-optimal matrices, square case      32—2 to 32—4
D-stability      19—5 to 19—7
Damped least squares      39—9 to 39—10
Dangling node      63—11
Daniel studies      44—4
Data Encryption Standard (DES) cryptographysystem      62—17
Data fitting      39—3 to 39—4
Data matrix      53—2 to 53—3
Data perturbations      38—2
Datta, Biswa Nath      37—1 to 37—21
Davidson’s method      43—10
Day, Jane      1—1 to 1—15
DCT      see «Discrete Fourier transform (DFT)»
de Oliveria studies      20—3
De Rijk’s row-cyclic pivoting      46—4
DeAlba, Luz M.      4—1 to 4—11
Decoder      61—2
Decoding      61—2
Decomposable tensors      13—3
Decomposition, direct solution of linear systems      38—7 to 38—15
Decomposition, high relative accuracy      46—7 to 46—10
Decomposition, least squares solutions      39—11 to 39—12
Decomposition, Mathematica software      73—18 to 73—19
Decomposition, matrix group      67—1
Decomposition, Morse, dynamical systems      56—7 to 56—9
Decomposition, rank revealing decomposition      39—11 to 39—12
Decomposition, semisimple and simple algebras      70—4
Decomposition, singular values      17—15
Decomposition, symmetric and Grassmann tensors      13—13
Decomposition, symmetric factorizations      38—15
Decomposition, tensors, multilinear algebra      13—7
Deconvolution, Fourier analysis      58—8
Deconvolution, functional and discrete theories      58—16
Decoupling Principle      59—1 59—2
Deeper properties      21—9 to 21—12
Defective matrices      4—6
Definite matrices      see «Positive definite matrices (PSD)»
Definite pencils      15—10
Deflation      42—2
Degenerate characteristics, sesquilinear forms      12—6
Degenerate characteristics, simplex method      50—12
Degree, certain integral domains      23—2
Degree, characters      68—5
Degree, control theory      57—2
Degree, convolutional codes      61—11
Degree, frequency-domain analysis      57—6
Degree, general properties      69—5
Degree, graphs      28—2
Degree, group representations      68—1
Degree, matrix group      67—1
Degree, matrix representations      68—3
Degree, max-plus permanent      25—9
Deletion, edges and vertices      28—4
Delsarte’s Linear Programming Bound      28—12

Delta function      58—2
demand, Mathematica software      73—24
Demmel — Kahan singular value decomposition      45—7 to 45—8
Demmel, James      75—1 to 75—23
Denardo algorithm      25—8
Denman — Beavers iteration      11—11
Dense matrices, fundamentals      43—1
Dense matrices, large-scale matrix computations      49—2
Dense matrices, software      77—2
Dense matrices, techniques      43—3 to 43—9
Depth, Jordan canonical form      6—3
Derangements      31—6
Derivation, Lie algebras      70—1
Derived algebra      70—3
Derogatory matrices      4—6
DES (Data Encryption Standard) cryptography system      62—17
Desargues’ theorem      65—8 65—9
Design matrices, D-optimal matrices      32—1
Design matrices, linear statistical models      52—8
Design, square case      32—2
det command, Matlab software      71—17
det function, Matlab software      71—3
Det, Mathematica software      73—10 73—11
Detection, control theory      57—2
Determinant, Maple software      72—5
Determinantal region      33—14
Determinantal relations      14—10 to 14—12
Determinants, advanced results      4—3 to 4—6
Determinants, connections      31—12 to 31—13
Determinants, fast matrix multiplication      47—10
Determinants, fundamentals      4—1 to 4—3
Determinants, invariants      23—5
Deterministic Markov decision process      25—3
Deterministic spectral estimation      64—14
Deutsch-Jozsa problem      62—9 to 62—11
Deutsch’s problem      62—8 to 62—9
Developer’HessenbergDecomposition’, Mathematica software      73—27
DGEMM BLAS subroutine package      42—21
DGKS mechanism      44—4
Dhillon, Inderjit S.      45—1 to 45—12
diag, Mathematica software      73—16
Diagonal entry      1—4 23—5
Diagonal matrices      1—4
Diagonal pattern      33—2
Diagonal product      27—10
Diagonal stability      19—9
Diagonalization, eigenvalue problems      15—10
Diagonalization, eigenvalues and eigenvectors      4—6 4—7
Diagonally dominant matrices      9—17
Diagonally scaled representation      46—10
Diagonally scaled totally unimodular (DSTU)      46—8 46—9
DiagonalMatrix, Mathematica software, eigenvalues      73—15 73—16
DiagonalMatrix, Mathematica software, matrices      73—6 73—8
Diagonals, square matrices      27—3
Diameter, eigenvalues      34—7
Diao, Zijian      62—1 to 62—19
Dias da Silva, Jose A.      13—1 to 13—26
Differentiable functions      56—5
Differential equations, constant coefficients      55—1 to 55—5
Differential equations, eigenvalues and eigenvectors      4—10 to 4—11
Differential equations, linear different equations      55—1 to 55—5
Differential equations, linear differential-algebraic equations      55—7 to 55—10 55—14
Differential equations, linear ordinary differential equations      55—5 to 55—6 55—10
Differential equations, linearization      56—19
Differential equations, stability      55—10 to 55—16
Differential quotient-difference (dqds) step      45—8 to 45—9
Differential-algebraic equations      55—1
Differential-algebraic equations of order      55—2
Digits, Maple software      72—14
Digraphs, adjacency matrix      29—3 to 29—4
Digraphs, cycle products      29—4 to 29—6
Digraphs, cyclic normal form      29—9 to 29—11
Digraphs, directed graphs      29—3 to 29—4
Digraphs, fundamentals      29—1 to 29—3
Digraphs, irreducible matrices      29—6 to 29—8
Digraphs, irreducible, imprimitive matrices      29—9 to 29—11
Digraphs, matrices      29—3 to 29—4
Digraphs, matrix completion problems      35—2
Digraphs, max-plus algebra      25—2
Digraphs, minimal connection      29—12 to 29—13
Digraphs, modeling and analyzing fill      40—11
Digraphs, nearly reducible matrices      29—12 to 29—13
Digraphs, nonnegative and stochastic matrices      9—2
Digraphs, P-, $P_{0, 1}-$ and $P_{0}$ -matrices      35—15 to 35—16
Digraphs, primitive digraphs and matrices      29—8 to 29—9
Digraphs, sign-pattern matrices      33—2
Digraphs, strongly connected digraphs      29—6 to 29—8
Digraphs, walk products      29—4 to 29—5
Dihedral interior angle      66—7
Dilations, numerical range      18—9 to 18—10
Dimension reduction      49—14 to 49—15
Dimension theorem, kernel      3—5
Dimension theorem, matrix range      2—6 to 2—9
Dimension theorem, null space      2—6 to 2—9
Dimension theorem, range      3—5
Dimension theorem, rank      2—6 to 2—9
Dimension, doubly stochastic matrices      27—10
Dimension, Euclidean point space      66—2
Dimension, Euclidean simplexes      66—7
Dimension, grading      70—9
Dimension, nonassociative algebra      69—1
Dimension, simultaneous similarity      24—8
Dimension, vector space      2—3
Dimensional projective spaces and subspaces      65—6
Dimensions, Mathematica software      73—6 73—7 73—27
Dirac’s bra-ket notation      62—2
Direct isometry      65—5 see
Direct solution, linear systems, fundamentals      38—1
Direct solution, linear systems, Gauss elimination      38—7 to 38—12
Direct solution, linear systems, LU decomposition      38—7 to 38—12
Direct solution, linear systems, orthogonalization      38—13 to 38—15
Direct solution, linear systems, perturbations      38—2 to 38—5
Direct solution, linear systems, QR decomposition      38—13 to 38—15
Direct solution, linear systems, symmetric factorizations      38—15 to 38—17
Direct solution, linear systems, triangular linear systems      38—5 to 38—7
Direct sum, block diagonal and triangular matrices      10—4
Direct sum, decompositions      2—4 to 2—6
Direct sum, direct sum decompositions      2—5
Direct sum, group representations      68—3
Direct sum, nonassociative algebra      69—3
Direct sum, semisimple and simple algebras      70—3
Direct Toeplitz solvers      48—4 to 48—5
Directed arcs, digraphs      29—1
Directed bigraphs      30—4
Directed digraphs      29—1
Directed edges      29—1
Directed graphs      29—3 to 29—4
Directed multigraph      29—2
Direction space, affine spaces      65—2
Direction, arrival estimation      64—15 to 64—18
Directory structure and contents      76—3
Dirichlet conditions      59—10
Discrete approximation      58—13
Discrete event systems      25—3 to 25—4
Discrete Fourier transform (DFT)      58—9
Discrete invariants      24—11
Discrete stochastic process      54—1
Discrete theory      58—2 to 58—17
Discrete time Fourier transform      64—2
Discrete variables      52—2
Discrete Wiener filtering problem      64—10
Discriminant coordinates      53—6
Disjoint matrix multiplication      47—8
dispersion      21—7
Dispersion matrix      52—3
Dissection strategy      40—16
Dissimilarity      53—13
Dissimilarity matrix      53—14
Distance bounds      61—5 to 61—6
Distance matrix      60—2

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