Relative Perturbation Theory: (I) Eigenvalue Variations
نویسنده
چکیده
In this paper, we consider how eigenvalues of a matrix A change when it is perturbed to e A = D 1AD2 and how singular values of a (nonsquare) matrix B change when it is perturbed to e B = D 1BD2, where D1 and D2 are assumed to be close to unitary matrices of suitable dimensions. We have been able to generalize many well-known perturbation theorems, including Ho man-Wielandt theorem and Weyl-Lidskii theorem. As applications, we obtained bounds for perturbations of graded matrices in both singular value problems and nonnegative de nite Hermitian eigenvalue problems.
منابع مشابه
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