## Some Sylvester-type Matrix Equations and Tensor Equations over the Quaternion Algebra

### When

April 6, 2018 | 2:30 - 3:30 p.m.

### Where

Campbell Hall 443

### Speaker

Zhuo-Heng He, Auburn University

### Abstract

Sylvester-type equations have many applications in neural network, robust control, output feedback control, the almost noninteracting control by measurement feedback problem, graph theory, and so on. In this talk, we consider some Sylvester-type matrix equations and tensor equations over the quaternion algebra. We present some necessary and sufficient conditions for the solvability to these Sylvester-type matrix equations and tensor equations over the quaternion algebra. Moreover, the general solutions to these quaternion matrix equations and tensor equations are explicitly given when they are solvable. We also provide some numerical examples to illustrate our results.