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 language | English |
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Article number | 32 |
Pages (from-to) | 465-475 |
Number of pages | 11 |
Journal | The Electronic Journal of Linear Algebra |
Volume | 31 |
Issue number | 1 |
DOIs | |
Publication status | Published - 11 Jul 2016 |
Keywords
- Common solution
- Linear matrix equations
- Rational matrix equations
- Triangular decoupling