Abstract
We consider a reduction of a nonhomogeneous linear system of first-order operator equations to a totally reduced system. Obtained results are applied to Cauchy problem for linear differential systems with constant coefficients and to the question of differential transcendency.
Highlights
Linear systems with constant coefficients are considered in various fields see 1–5
We denote by δk δk δk B the sum of its principal minors of order k 1 ≤ k ≤ n, ISRN Mathematical Analysis δki δki δki B the sum of its principal minors of order k containing ith column 1 ≤ i, k ≤ n
We consider a linear system of first-order A-operator equations with constant coefficients in unknowns xi, 1 ≤ i ≤ n, is
Summary
Linear systems with constant coefficients are considered in various fields see 1–5. In our paper 5 we use the rational canonical form and a certain sum of principal minors to reduce a linear system of first-order operator equations with constant coefficients to an equivalent, so called partially reduced, system. In this paper we obtain more general results regarding sums of principal minors and a new type of reduction. The obtained formulae of reduction allow some new considerations in connection with Cauchy problem for linear differential systems with constant coefficients and in connection with the differential transcendency of the solution coordinates
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