On Factorization and Calculation of Determinant of Block Matrices with Triangular Submatrices
Year: 2024
Type: article
Abstract: In this paper, we consider some block matrices of dimension $nm\times{nm}$ whose components are triangular matrices of dimension $n\times{n}$. We prove that the determinant of such block matrices is determined only by the diagonal elements of their submatrices and that this determinant is expressed as the multiplication of some subdeterminants. If the components of dimension $n\times{n}$ are all diagonal matrices, then we prove that such a block matrix can be written as a product of simpler matrices. Besides, we investigate the eigenvalues, the adjoint, and the inverse of such block matrices.
Source: Journal of New Theory
DOI: 10.53570/jnt.1545032
Authors: Ufuk Kaya, Fatma Altun
Institutions: Bitlis Eren University, Mi̇lli̇ Eği̇ti̇m Bakanliği
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4405964257