JP Journal of Algebra, Number Theory and Applications
Volume 41, Issue 1, Pages 35 - 47
(January 2019) http://dx.doi.org/10.17654/NT041010035 |
|
GENERAL Φ-HERMITIAN SOLUTION TO A SYSTEM OF QUATERNION MATRIX EQUATIONS
Mengyan Xie, Pingping Song and Zhiqing Zhang
|
Abstract: Let be the set of matrices over the quaternion algebra Let be the matrix obtained by applying Φ entrywise to the transposed matrix where and Φ is a nonstandard involution of is said to be Φ-Hermitian if where Φ is a nonstandard involution. In this paper, we consider the following system of quaternion matrix equations where A, B, C, and D are given quaternion matrices, the variable X is Φ-Hermitian. We give some necessary and sufficient conditions for the existence of a Φ-Hermitian solution to this system in terms of the ranks and Moore-Penrose inverses of the coefficient matrices. We also present an expression of the general Φ-Hermitian solution to this system when it is solvable. We also provide a numerical example to illustrate the main result. |
Keywords and phrases: quaternion, matrix equation, Moore-Penrose inverse, involution, Φ‑Hermitian solution.
|
|
Number of Downloads: 423 | Number of Views: 4583 |
|