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

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

2011-02-24

arxiv.org/abs/1102.5027v1

Mathematics

Spectral Theory

A note of 3 pages

Scientific paper

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.

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