In this paper, we derive the necessary and sufficient conditions for the quaternion matrix equation XA=B to have the least-square bisymmetric solution and give the expression of such solution when the solvability conditions are met. Futhermore, we consider the maximal and minimal inertias of the least-square bisymmetric solution to this equation. As applications, we derive sufficient and necessary conditions for XA=B to have the positive (nonnegative) definite least-square bisymmetric solution and the maximal (minimal) least-square bisymmetric solution.
Wang, Q., & Yu, G. (2013). The least-square bisymmetric solution to a quaternion matrix equation with applications. Bulletin of the Iranian Mathematical Society, 39(2), 239-257.
MLA
Q. Wang; G. Yu. "The least-square bisymmetric solution to a quaternion matrix equation with applications". Bulletin of the Iranian Mathematical Society, 39, 2, 2013, 239-257.
HARVARD
Wang, Q., Yu, G. (2013). 'The least-square bisymmetric solution to a quaternion matrix equation with applications', Bulletin of the Iranian Mathematical Society, 39(2), pp. 239-257.
VANCOUVER
Wang, Q., Yu, G. The least-square bisymmetric solution to a quaternion matrix equation with applications. Bulletin of the Iranian Mathematical Society, 2013; 39(2): 239-257.
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