Similarity and matrices of constant rank
If \(M\) and \(N\) are in \(M(n,\mathbb{C})\) and have the same rank, then there exist \(P\) and \(Q\) in \(GL(n,\mathbb{C})\) such that \(PMQ=N\). It is shown that \(P\) and \(Q\) can be chosen to be similar, or, equivalently, that there exist invertible matrices \(R\) and \(S\) such that \(RSMSR=N\).
scientific article; zbMATH DE number 1371412