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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

Householder reflections, tridiagonalization      42—6
Howell, Kenneth      58—1 to 58—20
HSEQR LAPACK subroutine      43—6
Hunacek, Mark      65—1 to 65—9
Hurwitz characteristics      57—9
Hurwitz command, Maple software      72—20
Hurwitz matrix      57—7
Hyperacute simplexes      66—10
Hyperbolic characteristics, linear dynamical systems      56—5
Hyperbolic characteristics, linearization      56—19
Hyperbolic characteristics, symmetric indefinite matrices      46—14
Hyperbolic Jacobi      46—15
Hyperlink matrix      63—10
Hyperplanes      66—2 66—2
Hypertext Induced Topic Search (HITS)      63—9
Hypotenuse, simplexes      66—10
IAP (inertiallyarbitrarypattern)      33—11
Ideal characteristics, algebras      69—18
Ideal characteristics, Lie algebras      70—1
Ideal characteristics, nonassociative algebra      69—3
Idempotence, general properties      69—5
Idempotence, invariant subspaces      3—6
Idempotence, nilpotence      2—12
Identity matrix, fundamentals      1—4 1—6
Identity matrix, matrices      1—4
Identity matrix, max-plus algebra      25—1
Identity matrix, systems of linear equations      1—13
Identity pattern      33—2
Identity, linear transformations      3—1
IdentityMatrix, Mathematica software, decomposition      73—19
IdentityMatrix, Mathematica software, eigenvalues      73—14
IdentityMatrix, Mathematica software, matrices      73—6 73—8
IdentityMatrix, Mathematica software, matrix algebra      73—11
IEPs      see «Inverse eigenvalue problems (IEPs)»
if statements, Matlab software      71—11
If, Mathematica software      73—8
IF-RCF (invariant factors rational canonical form) matrix      6—12
IIR (infinite impulse response)      64—2 64—3 64—6
Ill-conditioned properties, conditioning and condition numbers      37—7
Ill-conditioned properties, linear systems      37—10 to 37—11
Ill-conditioned properties, symmetric indefinite matrices      46—16
Image, kernel and range      3—5
Immanant      21—10 31—13
Implicit QR iteration      43—5
Implicit restarting      44—6 to 44—8
Implicitly restarted Arnoldi method (IRAM), Arnoldi factorization      44—2 to 44—4
Implicitly restarted Arnoldi method (IRAM), convergence      44—9 to 44—10
Implicitly restarted Arnoldi method (IRAM), fundamentals      44—1
Implicitly restarted Arnoldi method (IRAM), generalized eigenproblem      44—11
Implicitly restarted Arnoldi method (IRAM), implicit restarting      44—6 to 44—8
Implicitly restarted Arnoldi method (IRAM), Krylov methods      44—11 to 44—12
Implicitly restarted Arnoldi method (IRAM), Krylov subspace projection      44—1 to 44—2
Implicitly restarted Arnoldi method (IRAM), polynomial restarting      44—5 to 44—6
Implicitly restarted Arnoldi method (IRAM), restarting process      44—4 to 44—5
Implicitly restarted Arnoldi method (IRAM), sparse matrices      43—10
Implicitly restarted Arnoldi method (IRAM), spectral transformations      44—11 to 44—12
Implicitly restarted Arnoldi method (IRAM), subspaces      44—9 to 44—10
Implicitly shifted QR method      42—9 to 42—11
Imprimitive digraphs      29—9
Imprimitive gate      62—7
Improper divisors      23—2
Improper hydroplane      66—8
Improper point      66—8
Impulse response      64—2
imread command, Matlab software      71—15
Incidence matrix, binary matrices      31—5
Incidence matrix, matrix representations      28—7
Incidence matrix, square case      32—2
Incomplete Cholesky decomposition      41—11
Incomplete LU decomposition      41—11
Inconsistency, systems oflinear equations      1—9
Increment      74—2
Indecomposition      70—4
Indefinite matrices      8—6
Independence, direct sum decompositions      2—5
Independence, graph parameters      28—9
Independent and identical distribution      53—3
Index of imprimitivity, imprimitive matrices      29—10
Index of imprimitivity, irreducible matrices      9—3
Index of imprimitivity, reducible matrices      9—7
Index of primitivity      29—9
Index, Bezout domains      23—9
Index, Collatz-Wielandt sets      26—5
Index, doubly stochastic matrices      27—10
Index, eigenvectors      6—2
Index, linear differential-algebraic equations      55—7
Index, period      58—3
Index, polynomial interpolation      11—2
Index, reducible matrices      9—11
Indexing module      63—9
Indices, Web search      63—9
Indirect isometry      65—5
Individual condition number      15—1 15—10
Induced bases      2—5 13—15
Induced inner product      13—23
Induced subdigraphs      29—2
Induced subgraphs      28—2
Induction of characters      68—8 to 68—10
Inductive structure      27—4 to 27—6
Inequalities      see «Equalities and inequalities matrices»
Inequalities, irreducible matrices      9—5
Inequalities, reducible matrices      9—10
Inequalities, singular values and singular value inequalities      17—7 to 17—12
Inertia and stability, additive D-stability      19—7 to 19—8
Inertia and stability, fundamentals      19—1 to 19—2
Inertia and stability, inertia      19—2 to 19—3
Inertia and stability, Lyapunov diagonal stability      19—9 to 19—10
Inertia and stability, multiplicative D-stability      19—5 to 19—7
Inertia and stability, stability      19—3 to 19—5
Inertia set      33—11
Inertia, congruence      8—5
Inertia, matrix stability and inertia      19—2 to 19—3
Inertia, minimum rank      33—11 to 33—12
Inertia, preservation      19—5
Inertially arbitrary pattern (IAP)      33—11
Inexact preconditioners      41—16 to 41—17
Infeasibility      50—1
Inference, multivariate normal      53—4 to 53—5
Inference, statistical      53—12 to 53—13
Infinite dimensional      2—3
Infinite impulse response (IIR)      64—2 64—3 64—6
Infinite Markov chain      54—2
Infinitesimal element      21—11
infinity, Maple software      72—5
Infinity, Mathematica software      73—26
Information retrieval, fundamentals      63—1
Information retrieval, Google’s page rank      63—10 to 63—14
Information retrieval, latent semantic indexing      63—3 to 63—5
Information retrieval, nonnegative matrix factorization      63—5 to 63—8
Information retrieval, vector space method      63—1 to 63—3
Information retrieval, Web search      63—8 to 63—10
Inheritance principle      8—7
Inhomogeneity, Euclidean simplexes      66—8
Inhomogeneity, linear differential equations      55—2
Initial minor data sets      21—7
Initial parameter settings, ARPACK      76—6
Initial state vector      4—10
Initial value problem      55—2 56—2
Injective, kernel and range      3—5
inline command, Matlab software      71—11 to 71—12
Inner distribution      28—11
Inner product and inner product spaces, adjoints oflinear operators      5—5 to 5—6
Inner product and inner product spaces, floating point numbers      37—14
Inner product and inner product spaces, fundamentals      5—1 to 5—3
Inner product and inner product spaces, multilinear algebra      13—22 to 13—24
Inner product and inner product spaces, orthogonality relations      68—7
Innovations process      64—6
Innovations representation      64—6
Input space      57—2
Input, algorithms and efficiency      37—16

Insert, Mathematica software      73—13
Instability      see «Stability»
Instability, error analysis      37—18 to 37—21
Instability, numerical methods      37—18 to 37—21
Integers, Mathematica software      73—24
Integral domains, matrices over, Bezout domains      23—8 to 23—9
Integral domains, matrices over, certain integral domains      23—1 to 23—4
Integral domains, matrices over, fundamentals      23—1
Integral domains, matrices over, linear equations      23—8 to 23—9
Integral domains, matrices over, matrix equivalence      23—4 to 23—8
Integral domains, matrices over, strict equivalence, pencils      23—9 to 23—10
Integral kernels      59—10
Integrate, Mathematica software      73—1
Interactive software, freeware      77—1 to 77—3
Interactive software, Maple      72—1 to 72—21
Interactive software, Mathematica      73—1 to 73—27
Interactive software, Matlab      71—1 to 71—22
Interchange, classes of (0, 1)-matrices      27—7
Interchange, tournament matrices      27—9
interface, Maple software      72—7
Interior point methods      50—23 to 50—24
Interior solution      50—23
Interlaces      P—4
Interlacing inequalities      34—2
Interlacing, inequalities      8—3 to 8—4
Internal direct sum      69—3
Internal stability      57—15 see
International Standard Book Number (ISBN) code      61—4
Intersection number      28—11
Intersection, graphs      28—2
Intraclass correlation      52—9
inv command, Matlab software      71—17
inv function, Matlab software      71—3
Invariant factors rational canonical form (IF-RCF) matrix      6—12
Invariant factors, canonical forms      6—12 to 6—14
Invariant factors, inverse eigenvalue problems      20—3
Invariant factors, matrix equivalence      23—5
Invariant manifold theorem      56—20 56—21
Invariant polynomials, inverse eigenvalue problems      20—3
Invariant polynomials, matrix equivalence      23—5
Invariants, face      26—2
Invariants, group representations      68—1
Invariants, probability vectors      54—2
Invariants, random linear dynamical systems      56—14
Invariants, simultaneous similarity      24—8
Invariants, subspaces, projections      3—6 to 3—7
Invariants, vectors      54—2
Inverse discrete Fourier transform (inverse DFT)      58—9
Inverse eigenvalue problems (IEPs), $2\times 2$ block type      20—3 to 20—5
Inverse eigenvalue problems (IEPs), affine parameterized IEPs      20—10 to 20—12
Inverse eigenvalue problems (IEPs), fundamentals      20—1
Inverse eigenvalue problems (IEPs), nonnegative matrices      9—22 20—5
Inverse eigenvalue problems (IEPs), nonzero spectra, nonnegative matrices      20—7 to 20—8
Inverse eigenvalue problems (IEPs), numerical methods      20—11 to 20—12
Inverse eigenvalue problems (IEPs), prescribed entries      20—1 to 20—3
Inverse eigenvalue problems (IEPs), spectra, nonnegative matrices      20—6 to 20—10
Inverse eigenvalue problems (IEPs), trees      34—8
Inverse Fourier transform, Fourier analysis      58—2
Inverse Fourier transform, Karle — Hauptman matrix      60—8
Inverse iteration      42—2 42—14
Inverse Lanczos methods      16—11
Inverse M-matrices, completion problems      35—14 to 35—15
Inverse M-matrices, fundamentals      9—17
Inverse matrices      1—12
Inverse nonnegatives, inverse patterns      33—12
Inverse nonnegatives, M-matrices      9—17
Inverse nonnegatives, splitting theorems and stability      26—13
Inverse patterns      33—12 to 33—14
Inverse sign-pattern matrices      33—12 to 33—14
Inverse tridiagonal matrices      21—3
Inverse, Maple software      72—13
Inverse, Mathematica software, eigenvalues      73—16
Inverse, Mathematica software, linear systems      73—20 73—22
Inverse, Mathematica software, matrices      73—6 73—8
Inverse, Mathematica software, matrix algebra      73—10 73—11
Inverse, random vectors      52—4
Inverse-positivity matrices      9—17
InverseMatrixNorm, Mathematica software      73—10
Inversion, fast matrix multiplication      47—9 47—9
Inversion, isomorphism      3—7
Inversion, matrix equalities and inequalities      14—15 to 14—17
Invert spectral transformation mode, ARPACK      76—7
Inverted file, Web search      63—9
Invertibility, fundamentals
Invertibility, isomorphism      3—7
Invertibility, matrix equivalence      23—5
Invertible linear operators      67—1
Invertible matrices, decomposable tensors      13—7
Invertible matrices, fundamentals      1—12
Invertible matrices, LU factorizations      1—15
Invertible Matrix Theorem      1—12
Involution      69—2
IRAM      see «Implicitly restarted Arnoldi method (IRAM)»
Irreducibility, bimodules      69—6
Irreducibility, certain integral domains      23—2
Irreducibility, characterizing      9—3
Irreducibility, characters      68—5 68—6
Irreducibility, group representations      68—1
Irreducibility, imprimitive matrices      29—9 to 29—11
Irreducibility, matrix group      67—1
Irreducibility, matrix representations      68—3
Irreducibility, max-plus algebra      25—2
Irreducibility, modules      70—7
Irreducibility, Perron — Frobenius theorem      26—2
Irreducibility, simultaneous similarity      24—8
Irreducible classes      54—5 to 54—7
Irreducible components      27—5 to 27—6
Irreducible matrices, balancing      43—4
Irreducible matrices, digraphs      29—6 to 29—8
Irreducible matrices, fundamentals      9—2 to 9—7
Irreducible matrices, nonnegative matrices      9—2 to 9—7
ISBN (International Standard Book Number) code      61—4
Isolated invariant      56—7
Isolated vertex      28—2
Isometry, classical groups      67—5
Isometry, Euclidean spaces      65—4
Isomorphism, graphs      28—1
Isomorphism, Grassmannian manifolds      56—10
Isomorphism, group representations      68—1
Isomorphism, matrix representations      68—3
Isomorphism, nonassociative algebra      69—3
Isomorphism, nonsingularity characterization      3—7 to 3—8
Isoperimetric number      28—9
Isotalo, Jarkko      53—14
Iterative methods, function computation methods      11—10
Iterative methods, Krylov subspaces and preconditioners      41—2
Iterative methods, Toeplitz solvers      48—5
Iterative solution methods, linear solutions, CG convergence rates      41—14 to 41—15
Iterative solution methods, linear solutions, convergence rates      41—14 to 41—16
Iterative solution methods, linear solutions, error estimation      41—16 to 41—17
Iterative solution methods, linear solutions, finite precision arithmetic      41—16 to 41—17
Iterative solution methods, linear solutions, fundamentals      41—1 to 41—2
Iterative solution methods, linear solutions, GMRES convergence rates      41—15 to 41—16
Iterative solution methods, linear solutions, Hermitian problems      41—4 to 41—7
Iterative solution methods, linear solutions, inexact preconditioners      41—16 to 41—17
Iterative solution methods, linear solutions, Krylov subspaces      41—2 to 41—4
Iterative solution methods, linear solutions, MINRES convergence rates      41—14 to 41—15
Iterative solution methods, linear solutions, non-Hermitian problems      41—7 to 41—11
Iterative solution methods, linear solutions, non-optimal Krylov space methods      41—7 to 41—11
Iterative solution methods, linear solutions, optimal Krylov space methods      41—4 to 41—11
Iterative solution methods, linear solutions, preconditioned algorithms      41—12 to 41—14
Iterative solution methods, linear solutions, preconditioners      41—2 to 41—4 41—11
Iterative solution methods, linear solutions, stopping criteria      41—16 to 41—17
Jacobi identity, Akivis identity      69—19
Jacobi identity, Lie algebras      70—2
Jacobi identity, nonassociative algebra      69—2
Jacobi matrices      21—4
Jacobi methods, Krylov subspaces and preconditioners      41—3 to 41—4
Jacobi methods, symmetric matrix eigenvalue techniques      42—17 to 42—19
Jacobi rotation, Jacobi method      42—17

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