The Lidskii-Mirsky-Wielandt theorem - additive and multiplicative versions

Autor:	Chi-Kwong Li, Roy Mathias
Rok vydání:	1999
Předmět:	Combinatorics Computational Mathematics Pure mathematics Singular value Fundamental theorem Matrix splitting Applied Mathematics Multiplicative function Linear algebra Hermitian matrix Eigenvalues and eigenvectors Matrix decomposition Mathematics
Zdroj:	Numerische Mathematik. 81:377-413
ISSN:	0945-3245 0029-599X
DOI:	10.1007/s002110050397
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::a33edbd0ef6227ed045841f2c59f2dd6 https://doi.org/10.1007/s002110050397 Zobrazit plný text záznamu Full text from SpringerLink