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Ranks of solutions of the linear matrix equation \(AX + YB = C\). (English) Zbl 1129.15009

The author investigates the maximal and minimal ranks of a solution \((X,Y)\) to the complex matrix equation \(AX+YB=C\). Moreover, the maximal and minimal ranks of four real matrices \(X_0,X_1,Y_0,Y_1\) in a pair of solutions \(X=X_0+iX_1\) and \(Y=Y_0+iY_1\) to the matrix equation mentioned above are also presented.

MSC:

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

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