Summary.
We use a simple matrix splitting technique to give an elementary new proof of the Lidskii-Mirsky-Wielandt Theorem and to obtain a multiplicative analog of the Lidskii-Mirsky-Wielandt Theorem, which we argue is the fundamental bound in the study of relative perturbation theory for eigenvalues of Hermitian matrices and singular values of general matrices. We apply our bound to obtain numerous bounds on the matching distance between the eigenvalues and singular values of matrices. Our results strengthen and generalize those in the literature.
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Received November 20, 1996 / Revised version received January 27, 1998
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Li, CK., Mathias, R. The Lidskii-Mirsky-Wielandt theorem – additive and multiplicative versions . Numer. Math. 81, 377–413 (1999). https://doi.org/10.1007/s002110050397
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DOI: https://doi.org/10.1007/s002110050397