Some solutions to a third-order quaternion tensor equation

Abstract

The paper deals with the third-order quaternion tensor equation. Based on the Qt multiplication operation, we derive solvability conditions and also get the general solution, the least-squares solution, the minimum-norm solution and the minimum-norm least-squares solution of the tensor equation $ \mathcal{A} \ast_{\mathbb{Q}} \mathcal{X} = \mathcal{B} $. Finally, two numerical examples are presented.

Keywords

• tensor equation
• qt-product
• generalized inverse
• quaternion matrix
• least-squares solution
• minimum-norm solution