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

  • Written by  Volodymydr Prokip


Volodymyr Prokip

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).


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These are powerful results with a wide range of applications

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Scientific seminar, Aprill, 2015