Abstract：In this paper， starting from the concept of hyperbolic generalized quaternion， firstly， the study of hyperbolic generalized quaternion is transformed into the study of the matrix representation of hyperbolic generalized quaternion. Secondly， using the polar form of hyperbolic generalized quaternion， the De Moivre's theorems for the matrix representation of hyperbolic generalized quaternion in different cases are obtained. We discuss the internal relation among the powers of the hyperbolic generalized quaternion representation matrix， and extend the Euler's formula. Thirdly， the formula for solving the matrix representation equation of hyperbolic generalized quaternion is obtained. Finally， some examples to verify the correctness of the results are given.
2022, Vol. 56 
