A Sylvester-Type Matrix Equation over the Hamilton Quaternions with an Application

Abstract

We derive the solvability conditions and a formula of a general solution to a Sylvester-type matrix equation over Hamilton quaternions. As an application, we investigate the necessary and sufficient conditions for the solvability of the quaternion matrix equation, which involves η-Hermicity. We also provide an algorithm with a numerical example to illustrate the main results of this paper.

The Minimum-Norm Least Squares Solutions to Quaternion Tensor Systems

“…Nowadays, quaternion tensors are often used to solve problems in quantum mechanics, control theory, linear modeling, etc. [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”

A new generalization of a system of two-sided coupled Sylvester-like quaternion tensor equations

“…This is based on the various uses of quaternions, rank characterizations of some matrix expressions, matrix decompositions, the coupled Sylvester-like quaternion systems of matrix equations [2][3][4]6,8,14,[20][21][22][23][24]26,27,39,40,[47][48][49][50]52,54,55,57], and the theoretical studies surrounding Sylvester-like quaternion tensor equations. This paper investigates the consistency of and general solution to the following coupled two-sided Sylvester-like quaternion system of tensor equations:…”

The Solvability of a System of Quaternion Matrix Equations Involving ϕ-Skew-Hermicity

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