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Special Matrices and Their Applications in Numerical Mathematics

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ISBN-10: 0486466752

ISBN-13: 9780486466750

Edition: 2nd 2008

Authors: Miroslav Fiedler

List price: $19.95
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Description:

This revised and corrected second edition of a classic book on special matrices provides researchers in numerical linear algebra and students of general computational mathematics with an essential reference.
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Book details

List price: $19.95
Edition: 2nd
Copyright year: 2008
Publisher: Dover Publications, Incorporated
Publication date: 8/8/2008
Binding: Paperback
Pages: 384
Size: 5.25" wide x 8.25" long x 0.75" tall
Weight: 0.880
Language: English

Preface
Basic concepts of matrix theory
Matrices
Determinants
Nonsingular matrices. Inverse matrices
Schur complement. Factorization
Vector spaces. Rank
Eigenvectors, eigenvalues. Characteristic polynomial
Similarity. Jordan normal form
Symmetric Matrices. Positive Definite and Semidefinite Matrices
Euclidean and unitary spaces
Symmetric and Hermitian matrices
Orthogonal, unitary matrices
Gram-Schmidt orthonormalization
Positive definite matrices
Sylvester's law of inertia
Singular value decomposition
Graphs and Matrices
Digraphs
Digraph of a matrix
Undirected graphs. Trees
Bigraphs
Nonnegative Matrices. Stochastic and Doubly Stochastic Matrices
Nonnegative matrices
The Perron-Frobenius theorem
Cyclic matrices
Stochastic matrices
Doubly stochastic matrices
M-Matrices (Matrices of Classes K and K[subscript 0])
Class K
Class K[subscript 0]
Diagonally dominant matrices
Monotone matrices
Class P
Tensor Product of Matrices. Compound Matrices
Tensor product
Compound matrices
Matrices and polynomials. Stable Matrices
Characteristic polynomial
Matrices associated with polynomials
Bezout matrices
Hankel matrices
Toeplitz and Lowner matrices
Stable matrices
Band Matrices
Band matrices and graphs
Eigenvalues and eigenvectors of tridiagonal matrices
Norms and Their Use for Estimation of Eigenvalues
Norms
Measure of nonsingularity. Dual norms
Bounds for eigenvalues
Direct Methods for Solving Linear Systems
Nonsingular case
General case
Iterative Methods for Solving Linear Systems
General case
The Jacobi method
The Gauss-Seidel method
The SOR method
Matrix Inversion
Inversion of special matrices
The pseudoinverse
Numerical Methods for Computing Eigenvalues of Matrices
Computation of selected eigenvalues
Computation of all the eigenvalues
Sparse Matrices
Storing. Elimination ordering
Envelopes. Profile
Bibliography
Index