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On the symmetric solutions of a linear matrix equation. (English) Zbl 0622.15001
Let A be a real $$m\times n$$-matrix. An $$n\times m$$-matrix G is called a minimum-norm reflexive generalized inverse (MNRGI) of A, if the following relations hold: (i) $$AGA=A$$, (ii) $$GAG=G$$, (iii) $$GA=(GA)^ T$$. Partitioned MNRGIs are used to derive a necessary and sufficient condition for the consistency of the linear system (*) $$AX=B$$, $$X=X^ T$$, and to establish the explicit form of the general solution of (*) in that case. Furthermore, the dimension of the solution space to (*) is computed.
Reviewer: A.R.Kräuter

##### MSC:
 15A09 Theory of matrix inversion and generalized inverses 15A24 Matrix equations and identities
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