Abstract
The method of solving matrix linear equations and over commutative Bezout 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.
Highlights
The matrix linear equations play a fundamental role in many talks in control and dynamical systems theory 1–4
Roth 5 established the criterions of solvability of matrix equations 1.1, 1.2 whose coefficients A, B, and C are the matrices over a field F
In this paper we propose the method of solving matrix linear equations 1.2, 1.3 over a commutative Bezout domain
Summary
The matrix linear equations play a fundamental role in many talks in control and dynamical systems theory 1–4. Roth 5 established the criterions of solvability of matrix equations 1.1 , 1.2 whose coefficients A, B, and C are the matrices over a field F. It is not difficult to show, that these conditions of solvability hold for the matrix linear unilateral equation 1.3 over a commutative Bezout domain. The matrix equations 1.1 , 1.2 , 1.3 , where the coefficients A, B, and C are the matrices over a field F, reduce by means of the Kronecker product to equivalent systems of linear equations 15. In this paper we propose the method of solving matrix linear equations 1.2 , 1.3 over a commutative Bezout domain This method is based on the use of standard form of a pair of matrices with respect to generalized equivalence introduced in 20, 21 , and on congruences. We establish the criterions of uniqueness of particular solutions and write down the formulas of general solutions of such equations
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