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Least squares solutions with special structure to the linear matrix equation $AXB = C$. (English) Zbl 1230.15010
The equation $AXB=C$ with given matrices $A$, $B$, $C$ plays a very important role in matrix theory and applications and has been studied extensively. It is, in particular, connected with a certain growth curve model where it is important to be able to estimate the parameter matrix $X$. The authors derive the maximal and minimal ranks of the submatrices of a least squares solution matrix $X$ and from these formulas they derive necessary and sufficient conditions for the submatrices to be $0$ or other special forms. Finally, they obtain necessary and sufficient conditions for a least squares solution matrix $X$ to be Hermitian or locally Hermitian.

15A24Matrix equations and identities
Full Text: DOI
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