The least-square bisymmetric solution to a quaternion matrix equation with applications
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Abstract:
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.
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Journal title
volume 39 issue 2
pages 239- 257
publication date 2013-05-15
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