The eigenvalues and Moore-Penrose inverse of reduced biquaternion matrices

Abstract

The reduced biquaternions is a commutative algebra, which  can be thought of as a two-dimension space over  complex  field.  From this  point of view, we  introduce  two complex representations of  reduced biquaternion matrix  $A$.  We obtain the relationships  among these sets of eigenvalues of $A$ and its two complex representations.  Our results show that  each  reduced biquaternion matrix  $A$ has infinite  eigenvalues and different eigenvalues of $A$  may have the same eigenvector. We  also introduce  the concepts of determinant and the Moore-Penrose inverse of  reduced biquaternion matrices and obtain some properties of them.  As applications, we solve some reduced biquaternion linear equations. Some algorithms with  experimental  examples are provided to support our theoretical results.