A unification of some matrix factorization results
Let \(\mathbb{F}\) be a field with at least four elements. The author shows, if \(A\in M_n(\mathbb{F})\) is a nonsingular, nonscalar matrix, then \(A\) is similar to a matrix \(B\) that has a special \(LT\) factorization with all diagonal entries except one equal to \(1\) or a factorization \(L\left[\begin{smallmatrix} U&0\\ \star&d\end{smallmatrix}\right]\) where \(L\) and \(U\) are special lower and upper triangular matrices, respectively, with all diagonal entries equal to \(1\). He uses this theorem to unify the proofs of several matrix factorization theorems.
scientific article; zbMATH DE number 5612549
scientific article