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- W3083957377 abstract "Let $Ainmathbb{C}^{ntimes n}$ be a normal matrix with spectrum ${lambda_{i}}_{i=1}^{n}$, and let $widetilde{A}=A+Einmathbb{C}^{ntimes n}$ be a perturbed matrix with spectrum ${widetilde{lambda}_{i}}_{i=1}^{n}$. If $widetilde{A}$ is still normal, the celebrated Hoffman--Wielandt theorem states that there exists a permutation $pi$ of ${1,ldots,n}$ such that $big(sum_{i=1}^{n}|widetilde{lambda}_{pi(i)}-lambda_{i}|^{2}big)^{1/2}leq|E|_{F}$, where $|cdot|_{F}$ denotes the Frobenius norm of a matrix. This theorem reveals the strong stability of the spectrum of a normal matrix. However, if $A$ or $widetilde{A}$ is non-normal, the Hoffman--Wielandt theorem does not hold in general. In this paper, we present new upper bounds for $big(sum_{i=1}^{n}|widetilde{lambda}_{pi(i)}-lambda_{i}|^{2}big)^{1/2}$, provided that both $A$ and $widetilde{A}$ are general matrices. Some of our estimates improve or generalize the existing ones." @default.
- W3083957377 created "2020-09-14" @default.
- W3083957377 creator A5065249628 @default.
- W3083957377 date "2017-03-07" @default.
- W3083957377 modified "2023-10-18" @default.
- W3083957377 title "New upper bounds for the spectral variation of a general matrix" @default.
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- W3083957377 doi "https://doi.org/10.48550/arxiv.1703.02422" @default.
- W3083957377 hasPublicationYear "2017" @default.
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