On the diagonal of the matrices in a similarity class
Rings and Algebras
2012-08-30 v3
Abstract
Let A be an n by n matrix with entries in an arbitrary field, and c_1,...,c_n be scalars. We prove that if A is not a scalar multiple of the identity matrix, then the condition c_1+...+c_n=tr(A) is necessary and sufficient for A to be similar to a matrix with diagonal entries c_1,...,c_n.
Cite
@article{arxiv.1207.0631,
title = {On the diagonal of the matrices in a similarity class},
author = {Clément de Seguins Pazzis},
journal= {arXiv preprint arXiv:1207.0631},
year = {2012}
}
Comments
4 pages, withdrawn since the result has already been published with a similar proof