On the matrix equations UIXVJ = WI J for 1 ≤ I, J < K with I + J ≤ K

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Abstract

Conditions for the existence of a common solution X for the linear matrix equations UiXVj = Wi j for 1 ≤ i, j < k with i + j ≤ k, where the given matrices Ui, Vj,Wi j and the unknown matrix X have suitable dimensions, are derived. Verifiable necessary and sufficient solvability con-ditions, stated directly in terms of the given matrices and not using Kronecker products, are also presented. As an application, a version of the almost triangular decoupling problem is studied, and conditions for its solvability in transfer matrix and state space terms are presented.

Original languageEnglish
Article number32
Pages (from-to)465-475
Number of pages11
JournalThe Electronic Journal of Linear Algebra
Volume31
Issue number1
DOIs
Publication statusPublished - 11 Jul 2016

Keywords

  • Common solution
  • Linear matrix equations
  • Rational matrix equations
  • Triangular decoupling

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