Inverses of quasi-tridiagonal matrices
type: Item
instance of: scholarly article
title: Inverses of quasi-tridiagonal matrices
zbMATH Open document ID: 0537.15002
DOI: 10.1016/0024-3795(84)90123-X
author: S. A. H. Rizvi
published in: Linear Algebra and its Applications
publication date: 1984-01-01T00:00:00Z
review text: A blockmatrix \(T=[T_{ij}]\) with square blocks \(T_{ii}\) is quasi- triangular, if \(T_{ij}=0\) for \(| i-j|>1\). Explicit formulas for the inverses of quasi-triangular matrices are given. The inverses can be characterized by the quasi-triangle property: \(R=[R_{ij}]\) has the q.t.p. if all \(R_{ii}\) nonsingular and \(R_{ij}=R_{ik}R^{- 1}_{kk}R_{kj}\) for all \(i<k<j\) and for all \(i>k>j\). Theorem 3: Let K be a nonsingular block matrix whose diagonal blocks \(K_{ii} (i=2,...,n- 1)\) are nonsingular. Then K has the q.t.p. iff its inverse is quasi- tridiagonal.
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 3853273
zbMATH Keywords: blockmatrix
zbMATH Keywords: inverses
zbMATH Keywords: quasi triangular
zbMATH Keywords: quasi-triangle property
zbMATH Keywords: Explicit formulas for the inverses
reviewed by: Ludwig Elsner
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3853273