Matrix Perturbation TheoryThis book is a comprehensive survey of matrix perturbation theory, a topic of interest to numerical analysts, statisticians, physical scientists, and engineers. In particular, the authors cover perturbation theory of linear systems and least square problems, the eignevalue problem, and the generalized eignevalue problem as wellas a complete treatment of vector and matrix norms, including the theory of unitary invariant norms. |
Contents
Norms and Metrics | 49 |
Linear Systems and Least Squares Problems | 101 |
The Perturbation of Eigenvalues | 165 |
Copyright | |
5 other sections not shown
Other editions - View all
Common terms and phrases
A₁ acute perturbation approximation canonical angles Cmxn Cnxn column space compute condition number consistent matrix norm corresponding defined definite pair denote diagonal disks doubly stochastic doubly stochastic matrix eigen eigenspaces eigenvalue problem eigenvectors elements equation equivalent establish example exercise following theorem Frobenius norm Gerschgorin Hence Hermitian matrices inequality invariant subspace inverse Jordan Kahan L₁ least squares problem Lemma matrix pairs Moreover nonsingular nonzero normal normal matrices notation Notes and References orthogonal orthonormal P₁ permutation permutation matrix perturbation bounds perturbation theory positive definite Proof pseudo-inverse QR decomposition rank(A regular pair relative error residual bound result satisfying Schur Schur decomposition Show singular value decomposition solution spectral norm subsection SVA(A symmetric gauge function unitarily invariant norm unitary matrix upper triangular vector norm X₁ XHAX zero λη ση σι