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Distance from Idempotents to Nilpotents

Published online by Cambridge University Press:  20 November 2018

Gordon W. MacDonald
Gordon W. MacDonald*
Affiliation:
Dept. of Mathematics and Statistics, University of Prince Edward Island, Charlottetown, PEI, C1A 4P3 email: gmacdonald@upei.ca
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Abstract

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We give bounds on the distance from a non-zero idempotent to the set of nilpotents in the set of $n\,\times \,n$ matrices in terms of the norm of the idempotent. We construct explicit idempotents and nilpotents which achieve these distances, and determine exact distances in some special cases.

Keywords

47A1547D0315A30operatormatrixnilpotentidempotentprojection
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 59 , Issue 3 , 01 June 2007 , pp. 638 - 657
Copyright
Copyright © Canadian Mathematical Society 2007

References

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