Special Matrices And Their Applications In Numerical Mathematics Speciální Matice A Jejich Použití V Numerické Matematice. English

Miroslav Fiedler. Updated Translation Of: Speciální Matice A Jejich Použití V Numerické Matematice. Includes Index. Bibliography: P. 299-301. 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 This book begins with definitions of basic concepts of the theory of matrices and fundamental theorems. Subsequent chapters explore symmetric and Hermitian matrices, the mutual connections between graphs and matrices, and the theory of entrywise nonnegative matrices. The text introduces [capital italic]M-matrices, class [capital italic]K matrices, tensor products of matrices, compound matrices, and matricial representation of polynomials. The final chapters treat selected numerical methods for solving problems from the field of linear algebra, using the concepts and results explained in the preceding chapters