an:04008570
Zbl 0622.15001
Don, F. J. Henk
On the symmetric solutions of a linear matrix equation
EN
Linear Algebra Appl. 93, 1-7 (1987).
00152992
1987
j
15A09 15A24
matrix equation; symmetric solution; generalized inverse; Kronecker product; minimum-norm reflexive generalized inverse; consistency
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.
A.R.Kr??uter