On Elliptic Biquaternion Matrices

In this paper, the concept of the quaternionic adjoint matrix chi A of an elliptic biquaternion matrix A is introduced, which enable one to discuss the elliptic biquaternion problems through the quaternion ones. By this new concept, some fundamental problems, such as the right eigenvalues and eigenvectors, the singular value decomposition and the inverse can be investigated. Moreover, the least-squares solutions to the elliptic biquaternionic matrix equations AX = B and XA = B are derived, and the Sylvester-type elliptic biquaternion matrix equation AX - XB = C is also considered.

Automated summary

This paper introduces the concept of the quaternionic adjoint matrix of an elliptic biquaternion matrix, which allows for discussion of fundamental problems and solutions to related equations. The least-squares solutions to specific matrix equations are derived and a Sylvester-type equation is also considered.