Elementary triangular matrices and inverses of $k$-Hessenberg and triangular matrices

Abstract

We use elementary triangular matrices to obtain some factorization, multiplication, and inversion properties of triangular matrices. We also obtain explicit expressions for the inverses of strict $k$-Hessenberg matrices and banded matrices. Our results can be extended to the cases of block triangular and block Hessenberg matrices.

arXiv comment11 pages