On exponential of split quaternionic matrices. (English) Zbl 1426.15047

Erdoğdu, Melek; Özdemir, Mustafa

Appl. Math. Comput. 315, 468-476 (2017).

Summary: The exponential of a matrix plays an important role in the theory of Lie groups. The main purpose of this paper is to examine matrix groups over the split quaternions and the exponential map from their Lie algebras into the groups. Since the set of split quaternions is a noncommutative algebra, the way of computing the exponential of a matrix over the split quaternions is more difficult than calculating the exponential of a matrix over the real or complex numbers. Therefore, we give a method of finding exponential of a split quaternion matrix by its complex adjoint matrix.

MSC:

15B33	Matrices over special rings (quaternions, finite fields, etc.)
15A16	Matrix exponential and similar functions of matrices
17B45	Lie algebras of linear algebraic groups

Keywords:

quaternion; split quaternion; quaternion matrix

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