A Study on Commutative Elliptic Octonion Matrices

Abstract

In this study, firstly notions of similarity and consimilarity are given for commutative elliptic octonion matrices. Then the Kalman-Yakubovich s-conjugate equation is solved for the first conjugate of commutative elliptic octonions. Also, the notions of eigenvalue and eigenvector are studied for commutative elliptic octonion matrices. In this regard, the fundamental theorem of algebra and Gershgorin’s Theorem are proved for commutative elliptic octonion matrices. Finally, some examples related to our theorems are provided.

Keywords

• elliptic octonion matrices
• consimilarity
• gershgorin disk
• primary 12a27, 13a99
• secondary 15a18, 15b33