Nullities of submatrices of the Moore-Penrose inverse
type: Item
instance of: scholarly article
title: Nullities of submatrices of the Moore-Penrose inverse
zbMATH Open document ID: 0626.15004
DOI: 10.1016/0024-3795(87)90084-X
author: Donald W. Robinson
published in: Linear Algebra and its Applications
publication date: 1987-01-01T00:00:00Z
review text: If \(A=(A_{ij})\) and its Moore-Penrose inverse \(A^{\dag}=(B_{ij})\) are partitioned matrices with compatible splittings, then the paper gives lower and upper bounds on the difference of nullities \(\eta (B_{22})- \eta (A_{11})\). The bounds are expressed in terms of the number of rows and columns of A, its rank, and the nullities of certain blocks of the corresponding projection matrices \(AA^{\dag}\) and \(A^{\dag}A\). Proofs use the singular value decomposition theorem.
reviewed by: Sanjo Zlobec
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A45
zbMATH DE Number: 4017095
zbMATH Keywords: Moore-Penrose inverse
zbMATH Keywords: partitioned matrices
zbMATH Keywords: splittings
zbMATH Keywords: difference of nullities
zbMATH Keywords: singular value decomposition
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4017095