Field of values

Wednesday, January 27, 2016 - 9:00am - 9:50am
Michael Overton (New York University)
Crouzeix's conjecture is among the most intriguing developments in matrix theory in recent years. Made in 2004 by Michel Crouzeix, it postulates that, for any polynomial p and any matrix A, p(A) is less than or equal to 2 max(p(z): z in W(A)), where the norm is the 2-norm and W(A) is the field of values (numerical range) of A, that is the set of points attained by v*Av for some vector v of unit length. Remarkably, Crouzeix proved in 2007 that the inequality above holds if 2 is replaced by 11.08.
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