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The matrix linear unilateral and bilateral equations with two variables over commutative rings. (English) Zbl 1250.15022

Summary: The method of solving linear matrix equations \(AX + BY = C\) and \(AX + YB = C\) over commutative Bézout domains by means of standard form of a pair of matrices with respect to generalized equivalence is proposed. The formulas of general solutions of such equations are deduced. The criterions of uniqueness of particular solutions of such matrix equations are established.

MSC:

15A24 Matrix equations and identities
15B33 Matrices over special rings (quaternions, finite fields, etc.)
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