On the Marcus-Wang conjecture
Shu-An Hu · Linear and Multilinear Algebra · 1987
In [1], M. Marcus and B. Y. Wang cited the following conjecture: If kn A is an n-square matrix. Then A=0 if and only if per(U ∗ AU)=0 for all n× k-matrices U satisfying U ∗ U=Ik . In this paper we prove that the conjecture is true. Therefore we obtain the affirmative answer to a question about the numerical range of K{A).