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Real Representation Approach to Quaternion Matrix Equation Involving ϕ -Hermicity

Author

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  • Xin Liu
  • Huajun Huang
  • Zhuo-Heng He

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.

Suggested Citation

  • Xin Liu & Huajun Huang & Zhuo-Heng He, 2019. "Real Representation Approach to Quaternion Matrix Equation Involving ϕ -Hermicity," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-8, September.
    • Handle: RePEc:hin:jnlmpe:3258349
    DOI: 10.1155/2019/3258349
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