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

• Main Author: Verde-Star Luis
• Format: Article
• Language: English
• Published: De Gruyter 2015-11-01
• Series: Special Matrices
• Subjects: Triangular matrices; factorization; k-Hessenberg matrices; matrix inversion
• Online Access: http://www.degruyter.com/view/j/spma.2015.3.issue-1/spma-2015-0025/spma-2015-0025.xml?format=INT

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. An n × n lower triangular matrix is called elementary if it is of the form I + C, where I is the identity matrix and C is lower triangular and has all of its nonzero entries in the k-th column,where 1 ≤ k ≤ n.