FIRST-ORDER DISCRETE EQUATIONS WITH MATRIX VARIABLE NONCOMMUTATIVE COEFFICIENTS

Abstract

We consider the first-order matrix difference equation with variable noncommutative coefficients. In the algebra of matrix hypersequences, this equation corresponds to the first-order matrix algebraic differential equation with a regular singular point. It is proved that there exists a supstitution, which can reduce the equation under consideration to the Cauchy-type equation. This substitution can be found explicitly as the solution of some infinite system of matrix algebraic equations. The general solution of the equation is obtained in the algebra of matrix sequences.