Unitarily invariant class of matrices with powers without vanishing diagonal entries (with two figures)
Andrzej Pokrzywa · Linear and Multilinear Algebra · 1987
The largest unitarily invariant class of matrices such that all their powers have all nonzero entries in the diagonal is studied. It is shown that the eigenvalues of any matrix from this class lie on at most three half-lines beginning in the origin of the complex plane.