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A bound below for the convex hull of the spectrum of a matrix

By Eliahu Levy

Abstract

In this note the following is shown. Consider the quadratic form on (complex) matrices Q(A):=tr(A^2). Let A be such a matrix. Then an ellipse can be found, with the vector from center to focus determined by the value of Q at the traceless part of A, which must be contained in the convex hull of the spectrum of A.Comment: A note of 3 page

Topics: Mathematics - Spectral Theory
Year: 2011
OAI identifier: oai:arXiv.org:1102.5027
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