On the matrix equations UIXVJ = WI J for 1 ≤ I, J < K with I + J ≤ K
Journal Article
(2016)
Author(s)
Jacob van der Woude (TU Delft - Mathematical Physics)
Research Group
Mathematical Physics
DOI related publication
https://doi.org/10.13001/1081-3810.3312
To reference this document use:
https://resolver.tudelft.nl/uuid:63495357-a4f9-403b-b11a-1d0a332ee4ba
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Publication Year
2016
Language
English
Research Group
Mathematical Physics
Issue number
1
Volume number
31
Pages (from-to)
465-475
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.
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