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References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt147",{id:"formSmash:upper:j_idt147",widgetVar:"widget_formSmash_upper_j_idt147",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt148_j_idt150",{id:"formSmash:upper:j_idt148:j_idt150",widgetVar:"widget_formSmash_upper_j_idt148_j_idt150",target:"formSmash:upper:j_idt148:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

On the variation of the spectrum of a normal matrixPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 1996 (English)In: Linear Algebra and Its Applications, Vol. 246, 215-223 p.Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

1996. Vol. 246, 215-223 p.
##### National Category

Computer Science
##### Research subject

Numerical Analysis
##### Identifiers

URN: urn:nbn:se:umu:diva-20763ISBN: 0024-3795OAI: oai:DiVA.org:umu-20763DiVA: diva2:209448
#####

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Available from: 2009-03-25 Created: 2009-03-25 Last updated: 2009-03-25

Let A and (A) over tilde be two n x n normal matrices with spectra {lambda(j)} and {<(lambda)over tilde (j)>}. Then by the Hoffman-Wielandt theorem, there is a permutation pi of (1,...,n) such that root(n) Sigma(j = 1) \<(lambda)over tilde (pi(j))> - lambda(j)\(2) less than or equal to parallel to (A) over tilde - A parallel to(F), where parallel to parallel to(F) denotes the Frobenius norm. However, if A is normal but (A) over tilde nonnormal, it may be asked: How to relate the eigenvalues of (A) over tilde to those of A? An answer is given in this paper: There is a permutation pi of {1, 2,...,n} such that root(n) Sigma(j = 1) \<(lambda)over tilde (pi(j))> - lambda(j)\(2) less than or equal to root n parallel to (A) over tilde - A parallel to(F), and the factor root n is best possible. As a corollary, we have max (j) \<(lambda)over tilde (pi(j))> - lambda(j)\ less than or equal to n parallel to (A) over tilde - A parallel to(2).

References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1106",{id:"formSmash:lower:j_idt1106",widgetVar:"widget_formSmash_lower_j_idt1106",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1107_j_idt1109",{id:"formSmash:lower:j_idt1107:j_idt1109",widgetVar:"widget_formSmash_lower_j_idt1107_j_idt1109",target:"formSmash:lower:j_idt1107:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});