Further Results for Elliptic Biquaternions

Abstract

In this study, we show that the elliptic biquaternion algebra is algebraically isomorphic to the $2\times 2$ total elliptic matrix algebra and so, we get a faithful $2\times 2$ elliptic matrix representation of an elliptic biquaternion. Also, we investigate the similarity and the Moore-Penrose inverses of elliptic biquaternions by means of these matrix representations. Moreover, we establish universal similarity factorization equality (USFE) over the elliptic biquaternion algebra which reveals a deeper relationship between an elliptic biquaternion and its elliptic matrix representation. This equality and these representations can serve as useful tools for discussing many problems concerned with the elliptic biquaternions, especially for solving various elliptic biquaternion equations.

Keywords

• Elliptic Biquaternion,Matrix representation,Universal similarity factorization equality,Generalized inverse.

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