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

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

2011-08-29

arxiv.org/abs/1108.5522v1

Mathematics

Rings and Algebras

Scientific paper

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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