Solution to Problem 11387 [2008,758] : Capturing eigenvalues in an integral
O.P. Lossers · TU/e Research Portal · 2010
Proposed by Oskar Maria Baksalary, Adam Mickiewicz University, Poznan, Poland, and Götz Trenkler, Technische Universität Dortmund, Dortmund,Germany. Let Cn,n denote the set of n x n complex matrices. Determine the shortest interval [a, b] such that if P and Q in Cn,n are nonzero orthogonal projectors, that is, Hermitian idempotent matrices, then all eigenvalues of PQ + QP belong to [a, b].