Generalization of Mirsky's theorem on diagonals and eigenvalues of matrices
arXiv:1206.3744 · doi:10.1016/j.laa.2012.06.040
Abstract
Mirsky proved that, for the existence of a complex matrix with given eigenvalues and diagonal entries, the obvious necessary condition is also sufficient. We generalize this theorem to matrices over any field and provide a short proof. Moreover, we show that there is a unique companion-matrix-type solution for this problem.
arXiv comment3 pages