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I’m additionally fascinated when the algebraic method is applied to infinite objects”.

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

  • Written by  Volodymydr Prokip
  • 2 comments

 

Volodymyr Prokip

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 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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Department of Algebra and Logic
Faculty of Mechanics and Mathematics
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