Abstract:
In this talk we will revisit the following statement: The spectral norm of a (complex) matrix polynomial is bounded by a constant times the polynomial’s supremum norm taken over the matrix's numerical range. The surprising fact is that this constant can be chosen to be absolute and in particularly does not depend on the matrix. This was shown by Crouzeix in 2007 along with the conjecture that the optimal constant equals 2. This talk will give an introduction to this topic - which spans from numerical linear algebra over complex analysis to operator theory - and discuss recent achievements.