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

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On the matrix equations U_IXV_J = W_{I J} for 1 ≤ I, J < K with I + J ≤ K

Journal Article (2016)

Author(s)

Jacob van der Woude (TU Delft - Electrical Engineering, Mathematics and Computer Science)

Research Group

Mathematical Physics

Common solution Linear matrix equations Rational matrix equations Triangular decoupling

DOI related publication

https://doi.org/10.13001/1081-3810.3312 Final published version

To reference this document use

https://resolver.tudelft.nl/uuid:63495357-a4f9-403b-b11a-1d0a332ee4ba

More Info

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Publication Year

2016

Language

English

Research Group

Mathematical Physics

Issue number

1

Volume number

31

Article number

32

Pages (from-to)

465-475

Downloads counter

122

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.