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

Research output: Contribution to journalArticleScientificpeer-review


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
Issue number1
Publication statusPublished - 11 Jul 2016


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


Dive into the research topics of 'On the matrix equations U<sub>I</sub>XV<sub>J</sub> = W<sub>I J</sub> for 1 ≤ I, J < K with I + J ≤ K'. Together they form a unique fingerprint.

Cite this