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Elementary triangular matrices and inverses of k-Hessenberg and triangular matrices
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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. 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.
Title: Elementary triangular matrices and inverses of k-Hessenberg and triangular matrices
Description:
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.
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.
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