# Solutions of the matrix equation XA0 = A1 over a principal ideal domain with prescribed characteristic polynomials

- Written by Volodymydr Prokip
- 2 comments

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Department of Algebra

Pidstryhach Institute for Applied Problems

of Mechanics and Mathematics

National Academy of Sciences of Ukraine

**Abstract:**

We investigate the structure of solutions of a matrix equation *XA _{0} = A_{1}*, where

*A*,

_{1}*A*are

_{2}*n×m*matrices over a principal ideal domain

*R*with identity

*e≠0*and

*X*is unknown

*n×n*matrix. Let

*d(λ) = λ*be a monic polynomial of degree

^{n}+ d_{1}λ^{n-1}+ ... + d_{n-1}λ + d_{n}∈ R[λ]*n*. In this lecture we present conditions under which for the equation

*XA*there exists a solution

_{0}= A_{1}*X*with the characteristic polynomial

_{0}= D*d(λ)*.

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