On parallel summability of matrices
type: Item
instance of: scholarly article
title: On parallel summability of matrices
zbMATH Open document ID: 0589.15004
DOI: 10.1016/0024-3795(86)90126-6
published in: Linear Algebra and its Applications
publication date: 1986-01-01T00:00:00Z
review text: The authors use generalized inverses to characterize the parallel summability (p.s.) of matrices. If A and B are rectangular matrices of the same size, and if there exists C such that \(\{C^-\}=\{A^-+B^- \}\), then A and B are p.s. and \(C=P(A,B)\). (Here \(C^-\) denotes a weak generalized inverse of C and \(P(A,B)=A(A+B)^-B\) is the parallel sum of A and B.) A pair of almost positive definite (a.p.d.) matrices of the same type are p.s. and the parallel sum is a.p.d. of the same types as the summands. Finally, two ''saturated'' subclasses of a.p.d. matrices are identified.
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 3946353
zbMATH Keywords: generalized inverses
zbMATH Keywords: parallel summability
zbMATH Keywords: almost positive definite
author: Sujit Kumar Mitra
author: P. L. Odell
reviewed by: Sanjo Zlobec
MaRDI profile type: Publication
full work available at URL: 0024-3795(86)90126-6
OpenAlex ID: W1986864894
cites work: Series and parallel addition of matrices
cites work: Almost Definite Operators and Electro-mechanical Systems
cites work: Two Subspaces
cites work: Pseudoinverss of Postive Semidefeinite Matrices
cites work: Q5676331
cites work: On parallel sum and difference of matrices
cites work: The Fundamental Bordered Matrix of Linear Estimation and the Duffin-Morley General Linear Electromechanical Systems
cites work: Q5645536
cites work: Q5645537
cites work: Q5181471
Recommended article: On parallel sum of matrices
Recommended article: Q3029130
Recommended article: Q4706076
Recommended article: A remark on the characterization of the parallel sum of two matrices
Recommended article: On parallel sum of operators
Recommended article: Parallel sums and norm convergence
Recommended article: Q4877264
Recommended article: Q5000327
Recommended article: Q4355781
Recommended article: A note on the parallel sum
description: scientific article; zbMATH DE number 3946353