Department of Algebra
Pidstryhach Institute for Applied Problems
of Mechanics and Mathematics
National Academy of Sciences of Ukraine
We investigate the structure of solutions of a matrix equation XA0 = A1, where A1, A2 are n×m matrices over a principal ideal domain R with identity e≠0 and X is unknown n×n matrix. Let d(λ) = λn + d1λn-1 + ... + dn-1λ + dn ∈ R[λ] be a monic polynomial of degree n. In this lecture we present conditions under which for the equation XA0 = A1 there exists a solution X0 = D with the characteristic polynomial d(λ).