Analogs of Cramer's rule for the least squares solutions of some matrix equations

2011/08/29 by Ivan Kyrchei, Kyrchei, Ivan
Computer Science · Mathematics · #15A09 #15A24 #Algebraic and Geometric Analysis #FOS: Mathematics #Mathematics and Applications #Matrix Theory and Algorithms #Rings and Algebras (math.RA) #math.RA #msc:15A09 #msc:15A24

paper · pdf · doi:10.48550/arxiv.1108.5522

arxiv created 2011/08/29 · openalex publication_date 2011/08/29 · arxiv updated 2011/08/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The least squares solutions with the minimum norm of the matrix equations \rm \bf A\rm \bf X = \rm \bf B, \rm \bf X\rm \bf A = \rm \bf B and \rm \bf A\rm \bf X\rm \bf B =\rm \bf D are considered in this paper. We use the determinantal representations of the Moore - Penrose inverse obtained earlier by the author and get analogs of the Cramer rule for the least squares solutions of these matrix equations.

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