Generalization of Mirsky's theorem on diagonals and eigenvalues of matrices
Rings and Algebras
2013-01-22 v1
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.
Keywords
Cite
@article{arxiv.1206.3744,
title = {Generalization of Mirsky's theorem on diagonals and eigenvalues of matrices},
author = {Dragomir Z. Djokovic},
journal= {arXiv preprint arXiv:1206.3744},
year = {2013}
}
Comments
3 pages