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Title of article :
Counterexample to a conjecture of Elsner on the spectral variation of matrices Original Research Article
Author/Authors :
Yves Langlois، نويسنده , , Thomas Ransford، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2002
Pages :
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Abstract :
In 1985, Elsner proved that the Hausdorff distance Δ between the spectra of two n×n matrices A and B satisfiesimagewhere short parallel·short parallel denotes the operator norm with respect to the Euclidean norm on Cn. He further conjectured that the same inequality holds for all operator norms. We disprove this conjecture, and also the weaker conjecture where (short parallelAshort parallel+short parallelBshort parallel) is replaced by 2max(short parallelAshort parallel,short parallelBshort parallel).
Keywords :
Spectral variation , Operator norm
Journal title :
Linear Algebra and its Applications
Journal title :
Linear Algebra and its Applications
Serial Year :
Link To Document :