Matrix Perturbation Theory
This 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.
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The Singular Value Decomposition
Norms and Metrics
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applications approach approximation assume basis block bound called canonical angles chapter characterization columns components compute condition number consequence consider consistent contains continuous Corollary corresponding decomposition defined definite denote derive determine diagonal disks distance eigenvalue problem eigenvalues eigenvectors elements equality equation equivalent error establish example exercise fact following theorem function given gives Hence Hermitian important inequality introduce invariant subspace inverse Jordan least squares Lemma linear linear systems matrix norm Moreover multiple nonsingular nonzero normal notation Note obtain operator orthogonal orthonormal pair permutation perturbation perturbation bounds perturbation theory problem projection Proof properties prove rank rank(A reduced References regular residual result satisfying Show similarity simple singular values solution space spectral subsection suppose symmetric Theorem transformation triangular unique unitarily invariant norm unitary vector write zero