Real Representation Approach to Quaternion Matrix Equation Involving ϕ -Hermicity

Xin Liu, Huajun Huang and Zhuo-Heng He

Mathematical Problems in Engineering, 2019, vol. 2019, 1-8

Abstract:

For a quaternion matrix A , we denote by the matrix obtained by applying Ï• entrywise to the transposed matrix where Ï• is a nonstandard involution of quaternions. A is said to be Ï• -Hermitian or Ï• -skew-Hermitian if or , respectively. In this paper, we give a complete characterization of the nonstandard involutions Ï• of quaternions and their conjugacy properties; then we establish a new real representation of a quaternion matrix. Based on this, we derive some necessary and sufficient conditions for the existence of a Ï• -Hermitian solution or Ï• -skew-Hermitian solution to the quaternion matrix equation . Moreover, we give solutions of the quaternion equation when it is solvable.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:3258349

DOI: 10.1155/2019/3258349

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