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Hogben L. Ч Handbook of Linear Algebra
Hogben L. Ч Handbook of Linear Algebra

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Ќазвание: Handbook of Linear Algebra

јвтор: Hogben L.


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.

язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 2006

 оличество страниц: 1400

ƒобавлена в каталог: 30.06.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
ѕредметный указатель
$(\pm 1)$-matrices      31Ч8
$M_{0}$-matrices      35Ч12 to 35Ч13
(MRRR) multiple relatively robust representations      42Ч15 to 42Ч17
1hs, Mathematica software      73Ч20
Abelian, Lie algebras      70Ч2
Abs, Mathematica software      73Ч26
Absolute bound      28Ч11
Absolute errors, conditioning and condition numbers      37Ч7
Absolute errors, floating point numbers      37Ч13 37Ч16
Absolute irreducibility      67Ч1
Absolute matrix norms      37Ч4
Absolute values      17Ч1
Absolute vector norm      37Ч2
Absolute, simple graphs      36Ч9 to 36Ч10
Absorbing, irreducible classes      54Ч5
Absorbing, vector norms      37Ч3
Absorbing, vector seminorms      37Ч4
Access equivalence irreducible classes      54Ч5
Access equivalence, irreducible matrices      29Ч6 29Ч7
Access equivalence, max-plus eigenproblem      25Ч6
Access equivalence, nonnegative and stochastic matrices      9Ч2
Action, group representations      68Ч2
Active branch, algebraic connectivity      36Ч5
Active constraints      51Ч1
Acyclic matrices multiplicative D-stability      19Ч6
Acyclic matrices rank revealing decompositions      46Ч9
Ad-nilpotency      70Ч4
Ad-semisimple linear transformation      70Ч4
Adaptive filtering, signal processing      64Ч12 to 64Ч13
Addition      1Ч1 1Ч3
Additive coset      2Ч5
Additive D-stability      19Ч7 to 19Ч8
Additive identity axiom      1Ч1
Additive IEPs (AIEPs)      20Ч10
Additive inverse axiom      1Ч1
Additive preservers      22Ч7 to 22Ч8
Adjacency convex set points      50Ч13
Adjacency digraphs      29Ч3 to 29Ч4
Adjacency graphs      28Ч5 to 28Ч7
Adjacency Hermitian matrices      8Ч2
Adjacency linear preservers      22Ч7
Adjacency vertices      28Ч2
Adjoint linear transformation      51Ч3
Adjoint map, Lie algebras      70Ч2
Adjoints of linear operators, inner product spaces      5Ч5 to 5Ч6
Adjoints of linear operators, semidefinite programming      51Ч3
Adjoints, inner product spaces      13Ч22
Adjugates, determinants      4Ч3
Adjusting random vectors      52Ч4
Admissibility, control theory      57Ч2
Admittance matrix      28Ч7
Advanced linear algebra, bilinear forms      12Ч1 to 12Ч9
Advanced linear algebra, cone invariant departure, matrices      26Ч1 to 26Ч14
Advanced linear algebra, equalities, matrices      14Ч1 to 14Ч17
Advanced linear algebra, functions of matrices      11Ч1 to 11Ч12
Advanced linear algebra, inequalities, matrices      14Ч1 to 14Ч17
Advanced linear algebra, inertia, matrices      19Ч1 to 19Ч10
Advanced linear algebra, integral domains, matrices over      23Ч1 to 23Ч10
Advanced linear algebra, inverse eigenvalue problems      20Ч1 to 20Ч12
Advanced linear algebra, linear preserver problems      22Ч1 to 22Ч8
Advanced linear algebra, matrix equalities and inequalities      14Ч1 to 14Ч17
Advanced linear algebra, matrix perturbation theory      15Ч1 to 15Ч16
Advanced linear algebra, matrix stability and inertia      19Ч1 to 19Ч10
Advanced linear algebra, max-plus algebra      25Ч1 to 25Ч14
Advanced linear algebra, multilinear algebra      13Ч1 to 13Ч26
Advanced linear algebra, numerical range      18Ч1 to 18Ч11
Advanced linear algebra, perturbation theory, matrices      15Ч1 to 15Ч16
Advanced linear algebra, pseudospectra      16Ч1 to 16Ч15
Advanced linear algebra, quadratic forms      12Ч1 to 12Ч9
Advanced linear algebra, sesquilinear forms      12Ч1 to 12Ч9
Advanced linear algebra, similarity of matrix families      23Ч1 to 23Ч10
Advanced linear algebra, singular values and singular value inequalities      17Ч1 to 17Ч15
Advanced linear algebra, stability, matrices      19Ч1 to 19Ч10
Advanced linear algebra, total negativity, matrices      21Ч1 to 21Ч12
Advanced linear algebra, total positivity, matrices      21Ч1 to 21Ч12
Affine algebraic variety      24Ч8
Affine function      50Ч1
Affine parameterized IEPs (PIEPs)      20Ч10 to 20Ч12
Affine subspace determination      65Ч2
Affine-independence      65Ч2
AIEPs (additive IEPs)      20Ч10
Aissen studies      21Ч12
Aitken estimator      52Ч8
Akian, Marianne      25Ч1 to 25Ч14
Akivis algebra      69Ч16 to 69Ч17
Albert algebra      69Ч4 69Ч14
Alexandroff inequality      25Ч10
AlexandrovТs inequality      31Ч2
Algebra      PЧ1
Algebra applications      see also ЂNonassociative algebraї
Algebra applications, group representations      68Ч1 to 68Ч11
Algebra applications, Lie algebras      70Ч1 to 70Ч10
Algebra applications, matrix groups      67Ч1 to 67Ч7
Algebra applications, nonassociative algebra      69Ч1 to 69Ч25
Algebraic aspects, least squares solutions      39Ч4 to 39Ч5
Algebraic connectivity, absolute, simple graphs      36Ч9 to 36Ч10
Algebraic connectivity, Fiedler vectors      36Ч7 to 36Ч9
Algebraic connectivity, generalized Laplacian      36Ч10 to 36Ч11
Algebraic connectivity, matrix representations      28Ч7
Algebraic connectivity, multiplicity      36Ч10 to 36Ч11
Algebraic connectivity, simple graphs      36Ч1 to 36Ч4 36Ч9
Algebraic connectivity, trees      36Ч4 to 36Ч6
Algebraic connectivity, weighted graphs      36Ч7 to 36Ч9
Algebraic eigenvalues      25Ч9 see
Algebraic function, matrix similarities      24Ч1
Algebraic geometric Goppa (AG) code      61Ч10
Algebraic multigrid, preconditioners      41Ч11
Algebraic multiplicity      4Ч6
Algebraic Riccati equation (ARE)      57Ч10 57Ч12
Algorithms      see specific algorithm
Algorithms, Arbitrary Precision Approximating (APA)      47Ч6
Algorithms, Arnoldi      41Ч7
Algorithms, BiCGSTAB      41Ч8
Algorithms, biconjugate gradient (BCG/BiCG)      41Ч7 49Ч13
Algorithms, bilinear noncommutative      47Ч2
Algorithms, bit flipping algorithm      61Ч11
Algorithms, Conjugate Gradient (CG)      41Ч4 41Ч6
Algorithms, conjugate gradient squared (CGS)      41Ч8
Algorithms, Denardo      25Ч8
Algorithms, error analysis      37Ч16 to 37Ч17
Algorithms, ESPRIT      64Ч17
Algorithms, EuclidТs      23Ч2
Algorithms, fast matrix multiplication      47Ч2 to 47Ч7
Algorithms, Full Orthogonalization Method (FOM)      41Ч7
Algorithms, Generalized Minimal Residual (GMRES)      41Ч7 49Ч13
Algorithms, Lanczos algorithm      41Ч4 to 41Ч5
Algorithms, least squares solutions      39Ч6 to 39Ч7
Algorithms, left-preconditioned BiCGSTAB algorithm      41Ч12
Algorithms, Levinson-Durbin algorithm      64Ч8
Algorithms, Minimal Residual (MINRES)      41Ч4 41Ч6
Algorithms, MUSIC      64Ч17
Algorithms, non-Hermitian Lanczos algorithm      41Ч7
Algorithms, noncommutative      47Ч2
Algorithms, policy iteration      25Ч7
Algorithms, power algorithm      25Ч7
Algorithms, preconditioned conjugate gradient (PCG)      41Ч13
Algorithms, quasi-minimal residual (QMR)      41Ч8 49Ч13
Algorithms, restarted GMRES algorithm      41Ч7
Algorithms, singular value decomposition      45Ч4 to 45Ч12
Algorithms, transpose-free quasi-minimal residual (TFQMR)      49Ч14
Algorithms, two-sided Lanczos algorithm      41Ч7
All-ones matrix      52Ч4
Allowing characteristics, random vectors      52Ч4
Allowing characteristics, sign-pattern matrices      33Ч9 to 33Ч11
Alphabet, coding theory      61Ч1
Alt multiplication      13Ч17 to 13Ч19
Alternate path, single arc      35Ч14
Alternating bilinear forms      12Ч5 to 12Ч6
Alternative algebras      69Ч2 69Ч10
Alternative bimodule      69Ч10
Alternator      13Ч12
AMG code      41Ч12
Analysis applications, control theory      57Ч1 to 57Ч17
Analysis applications, differential equations      55Ч1 to 55Ч16
Analysis applications, dynamical systems      56Ч1 to 56Ч21
Analysis applications, Fourier analysis      58Ч1 to 58Ч20
Analysis applications, LTI systems      57Ч7 to 57Ч10
Analysis applications, stability      55Ч1 to 55Ч16
Analytical similarity      24Ч1
Analyzing fill      40Ч10 to 40Ч13
Angles, inner product spaces      5Ч1
Annihilator      3Ч8 to 3Ч9
Anti-identity matrices      48Ч2
Anticommutative algebra      69Ч2
Anticommutativity      70Ч2
Anticommutator      69Ч3
Antisymmetric maps      13Ч10 to 13Ч12
Antisymmetry      12Ч5
Aperiodicity, characterizing      9Ч3
Aperiodicity, irreducible classes      54Ч5
Aperiodicity, irreducible matrices      9Ч3
Aperiodicity, reducible matrices      9Ч7
Append, Mathematica software, linear systems      73Ч23
Append, Mathematica software, matrices manipulation      73Ч13
Append, Mathematica software, vectors      73Ч3
AppendColumns, Mathematica software      73Ч13
Appending, vertices      36Ч3
AppendRows, Mathematica software      73Ч13
Applications, algebra, group representations      68Ч1 to 68Ч11
Applications, algebra, Lie algebras      70Ч1 to 70Ч10
Applications, algebra, matrix groups      67Ч1 to 67Ч7
Applications, algebra, nonassociative algebra      69Ч1 to 69Ч25
Applications, analysis, control theory      57Ч1 to 57Ч17
Applications, analysis, differential equations      55Ч1 to 55Ч16
Applications, analysis, dynamical systems      56Ч1 to 56Ч21
Applications, analysis, Fourier analysis      58Ч1 to 58Ч20
Applications, analysis, stability      55Ч1 to 55Ч16
Applications, biological sciences      60Ч1 to 60Ч13
Applications, computer science, coding theory      61Ч1 to 61Ч13
Applications, computer science, information retrieval      63Ч1 to 63Ч14
Applications, computer science, quantum computation      62Ч1 to 62Ч19
Applications, computer science, signal processing      64Ч1 to 64Ч18
Applications, computer science, Web searches      63Ч1 to 63Ч14
Applications, fast matrix multiplication      47Ч9 to 47Ч10
Applications, geometry, Euclidean geometry      66Ч1 to 66Ч15
Applications, geometry, geometry      65Ч1 to 65Ч9
Applications, optimization, linear programming      50Ч1 to 50Ч24
Applications, optimization, semidefinite programming      51Ч1 to 51Ч11
Applications, physical sciences      59Ч1 to 59Ч11
Applications, probability and statistics, linear statistical models      52Ч1 to 52Ч15
Applications, probability and statistics, Markov chains      54Ч1 to 54Ч14
Applications, probability and statistics, multivariate statistical analysis      53Ч1 to 53Ч14
Applications, probability and statistics, random vectors      52Ч1 to 52Ч15
Applications, semidefinite programming      51Ч9 to 51Ч11
Apply, Mathematica software      73Ч3 73Ч5 73Ч27
Approximate Jordan form, Maple software      72Ч15
Approximate prescribed-line-sum scalings      9Ч21 to 9Ч22
Approximation, fast matrix multiplication      47Ч6 to 47Ч7
Approximation, linear programming      50Ч20 to 50Ч23
Approximation, orthogonal projection      5Ч7
ArbitraryPrecision Approximating (APA) algorithms      47Ч6
ArcSin, Mathematica software      73Ч26
ARE      see ЂAlgebraic Riccati equation (ARE)ї
Arithmetic Euclidean vector space      66Ч1
Arm, stars      34Ч10
Arnold Hypothesis, Strong      28Ч9 28Ч10
Arnoldi algorithm      41Ч7 41Ч8
Arnoldi decomposition      16Ч11
Arnoldi factorization, implicitly restarted Arnoldi method      44Ч2 to 44Ч4
Arnoldi factorization, pseudospectra      16Ч3
Arnoldi matrices      49Ч11
Arnoldi method      see ЂImplicitly restarted Arnoldi method (IRAM)ї
Arnoldi method, eigenvalue computations      49Ч12
Arnoldi method, implicit restarting      44Ч6
Arnoldi method, large-scale matrix computations      49Ч10 to 49Ч11
Arnoldi method, sparse matrices      43Ч9 43Ч11
Arnoldi vectors, Arnoldi factorization      44Ч3
Arnoldi vectors, Arnoldi process      49Ч11
ARPACK subroutine package, computational modes      76Ч8 to 76Ч9
ARPACK subroutine package, directory structure and contents      76Ч3
ARPACK subroutine package, fundamentals      76Ч1 to 76Ч2 76Ч4
ARPACK subroutine package, Lanczos methods      42Ч21
ARPACK subroutine package, MatlabТs EIGS      76Ч9 to 76Ч10
ARPACK subroutine package, naming conventions      76Ч3 to 76Ч4
ARPACK subroutine package, precisions      76Ч3 to 76Ч4
ARPACK subroutine package, pseudospectra computation      16Ч12
ARPACK subroutine package, reverse communication      76Ч2
ARPACK subroutine package, setup of problem      76Ч5 to 76Ч7
ARPACK subroutine package, sparse matrices      43Ч9
ARPACK subroutine package, types      76Ч3 to 76Ч4
ARPACK subroutine package, use      76Ч7 to 76Ч8
Array arithmetic, Maple software      72Ч8
Array, Maple software      72Ч1 72Ч2
Array, Mathematica software, matrices      73Ч6
Array, Mathematica software, vectors      73Ч3 73Ч4
ArrayPlot, Mathematica software, fundamentals      73Ч27
ArrayPlot, Mathematica software, matrices      73Ч7 73Ч9
ArrayRules, Mathematica software      73Ч6
Arrays, Fourier analysis      58Ч2
Arrays, manifold      64Ч16
Arrays, Maple software      72Ч8 to 72Ч9
Arrays, response vector      64Ч16
Arrays, response vector, Maple software      72Ч8 72Ч9
Arrival estimation direction      64Ч15 to 64Ч18
Arrow, Mathematica software      73Ч5
ArtinТs theorem      69Ч3 69Ч11
AspectRatio, Mathematica software      73Ч27
Assignment polytope      27Ч10
Associated divisor      61Ч10
Associated linear programming      50Ч14
Associated maps      13Ч19 to 13Ч20
Association schemes, graphs      28Ч11 to 28Ч12
Associations, generalized stars      34Ч11
Associative algebra      69Ч2
Associative center      69Ч5
Associative enveloping algebra      69Ч13
Associative nucleus      69Ч5
Associativity axiom      1Ч1 1Ч2
Associator ideal      69Ч5
Associator, nonassociative algebra      69Ч2
Asymmetric digraphs      35Ч2 see
Asymptotic spectrum      47Ч8
Asymptotic stability, control theory      57Ч2
Asymptotic stability, linear differential-algebraic equations      55Ч14
Asymptotic stability, linear ordinary differential equations      55Ч10
Asymptotic stability, LTI systems      57Ч7
Asymptotics, matrix powers      25Ч8 to 25Ч9
ATLAST M-file collection      71Ч20
Attractor-repeller decompositions      56Ч7
Augmented matrices, Bezout domains      23Ч9
Augmented matrices, systems of linear equations      1Ч9 1Ч11
Augmented systems, least squares solution      39Ч4
Autocorrelation matrix      64Ч5
Autocorrelation sequence      64Ч4
Automatic, Mathematica software, fundamentals      73Ч27
Automatic, Mathematica software, singular values      73Ч17
Automorphism, Lie algebras      70Ч1
Automorphism, ring, linear preservers      22Ч7
Autonomy, control theory      57Ч2
Backward errors, analysis      37Ч20
Backward errors, numerical stability and instability      37Ч18 37Ч20
Backward errors, one-sided Jacobi SVD algorithm      46Ч2
Backward stability, numerical stability and instability      37Ч18
Backward stability, numerical stability and instability, one-sided Jacobi SVD algorithm      46Ч2
BackwardsSubstitute, Maple software      72Ч9
Bad columns      50Ч8
Bad rows      50Ч8
Badly-conditioned data      37Ч7
Bai, Zhaojun      75Ч1 to 75Ч23
Bailey, D.      47Ч5
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