A note on solutions of linear systems

In this paper we will consider Rohde's general form of {1}-inverse of a matrix A. The necessary and sufficient condition for consistency of a linear system Ax=c will be represented. We will also be concerned with the minimal number of free parameters in Penrose's formula x = A^(1) c + (I -...

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Bibliographic Details
Published in:arXiv.org 2013-07
Main Authors: Malesevic, Branko, Jovovic, Ivana, Makragic, Milica, Radicic, Biljana
Format: Article
Language:English
Subjects:
Linear systems
Mathematical analysis
Matrix methods
Online Access:Get full text
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Summary:In this paper we will consider Rohde's general form of {1}-inverse of a matrix A. The necessary and sufficient condition for consistency of a linear system Ax=c will be represented. We will also be concerned with the minimal number of free parameters in Penrose's formula x = A^(1) c + (I - A^(1)A)y for obtaining the general solution of the linear system. This results will be applied for finding the general solution of various homogenous and non-homogenous linear systems as well as for different types of matrix equations.
ISSN:2331-8422