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.

中文翻译：

---

椭圆双四元数矩阵

本文介绍了椭圆双四元数矩阵A的四元数伴随矩阵\（\ chi _A \）的概念，使人们能够通过四元数来讨论椭圆双四元数问题。通过这个新概念，可以研究一些基本问题，例如正确的特征值和特征向量，奇异值分解和逆。此外，推导椭圆双四元数矩阵方程\（AX = B \）和\（XA = B \）的最小二乘解，而Sylvester型椭圆双四元数矩阵方程\（AX-XB = C \）为也考虑过。