Special Matrices and Their Applications in Numerical Mathematics

Title......Page 0001_0001.djvu
Preface......Page 0003_0001.djvu
Contents......Page 0007_0001.djvu
Summary of Notation......Page 0011_0001.djvu
Matrices......Page 0015_0001.djvu
Determinants......Page 0020_0001.djvu
Nonsingular matrices. Inverse matrices......Page 0025_0001.djvu
Schur complement. Factorization......Page 0029_0001.djvu
Vector spaces. Rank......Page 0034_0001.djvu
Eigenvectors, eigenvalues. Characteristic polynomial......Page 0036_0001.djvu
Similarity. Jordan normal form......Page 0038_0001.djvu
Exercises......Page 0046_0001.djvu
Euclidean and unitary spaces......Page 0049_0001.djvu
Symmetric and Hermitian matrices......Page 0051_0001.djvu
Orthogonal and unitary matrices......Page 0053_0001.djvu
Gram-Schmidt orthonormalization. Schur's theorem......Page 0057_0001.djvu
Positive definite and positive semidefinite matrices......Page 0061_0001.djvu
Sylvester's law of inertia......Page 0067_0001.djvu
Singular value decomposition......Page 0069_0001.djvu
Exercises......Page 0073_0001.djvu
Digraphs......Page 0075_0001.djvu
Digraph of a matrix......Page 0080_0001.djvu
Undirected graphs. Trees......Page 0083_0001.djvu
Bigraphs......Page 0090_0001.djvu
Exercises......Page 0095_0001.djvu
Nonnegative matrices......Page 0097_0001.djvu
The Perron-Frobenius theorem......Page 0100_0001.djvu
Cyclic matrices......Page 0105_0001.djvu
Stochastic matrices......Page 0115_0001.djvu
Doubly stochastic matrices......Page 0117_0001.djvu
Exercises......Page 0121_0001.djvu
5. M-Matrices (Matrices of Classes K and Ko)......Page 0122_0001.djvu
Class K......Page 0124_0001.djvu
Class Ko......Page 0131_0001.djvu
Diagonally dominant matrices......Page 0136_0001.djvu
Monotone matrices......Page 0140_0001.djvu
Class P......Page 0141_0001.djvu
Exercises......Page 0145_0001.djvu
6. Tensor Product of Matrices. Compound Matrices......Page 0146_0001.djvu
Tensor product......Page 0147_0001.djvu
Compound matrices......Page 0152_0001.djvu
Exercises......Page 0165_0001.djvu
Characteristic polynomial......Page 0167_0001.djvu
Matrices associated with polynomials......Page 0170_0001.djvu
Bezout matrices......Page 0174_0001.djvu
Hankel matrices......Page 0177_0001.djvu
Toeplitz and Löwner matrices......Page 0187_0001.djvu
Stable matrices......Page 0188_0001.djvu
Exercises......Page 0196_0001.djvu
Band matrices and graphs......Page 0199_0001.djvu
Eigenvalues and eigenvectors of tridiagonal matrices......Page 0205_0001.djvu
Exercises......Page 0210_0001.djvu
Norms......Page 0211_0001.djvu
Measure of nonsingularity. Dual norms......Page 0219_0001.djvu
Bounds for eigenvalues......Page 0225_0001.djvu
Exercises......Page 0240_0001.djvu
Nonsingular case......Page 0241_0001.djvu
General case......Page 0249_0001.djvu
Exercises......Page 0254_0001.djvu
11. Iterative Methods for Solving Linear Systems......Page 0255_0001.djvu
The Jacobi method......Page 0257_0001.djvu
The Gauss-Seidel method......Page 0259_0001.djvu
The SOR method......Page 0262_0001.djvu
Exercises......Page 0272_0001.djvu
Inversion of special matrices......Page 0274_0001.djvu
The pseudo inverse......Page 0280_0001.djvu
Exercises......Page 0281_0001.djvu
Computation of selected eigenvalues......Page 0283_0001.djvu
Computation of all the eigenvalues......Page 0286_0001.djvu
Exercises......Page 0294_0001.djvu
Storing. Elimination ordering......Page 0296_0001.djvu
Envelopes. Profile......Page 0304_0001.djvu
Exercises......Page 0308_0001.djvu
Bibliography......Page 0309_0001.djvu
Subject Index......Page 0313_0001.djvu