The linear preservers of real diagonalizable matrices
arXiv:1007.1983 · doi:10.1016/j.laa.2011.03.014
Abstract
Using a recent result of Bogdanov and Guterman on the linear preservers of pairs of simultaneously diagonalizable matrices, we determine all the automorphisms of the vector space M_n(R) which stabilize the set of diagonalizable matrices. To do so, we investigate the structure of linear subspaces of diagonalizable matrices of M_n(R) with maximal dimension.
14 pages