Home > ELA > Vol. 31 (2016)

#### Keywords

Linear matrix equations, common solution, rational matrix equations, triangular decoupling.

#### Abstract

Conditions for the existence of a common solution X for the linear matrix equations U_iXV_j W_{ij} for 1 \leq i,j \leq k with i\leq j \leq k, where the given matrices U_i,V_j,W_{ij} and the unknown matrix X have suitable dimensions, are derived. Verifiable necessary and sufficient solvability conditions, 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.

#### Recommended Citation

van der Woude, Jacob.
(2016),
"On the matrix equations U_iXV_j W_{i j} for 1 \leq i; j \leq k with i +j \leq k",
*Electronic Journal of Linear Algebra*,
Volume 31, pp. 465-475.

DOI: http://dx.doi.org/10.13001/1081-3810.3312

*Abstract*