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The extreme inertias of the least-square bisymmetric solution to a quaternion matrix equation with applications

Articles in Press, Accepted Manuscript , Available Online from 23 December 2011  XML
Document Type: Research Paper
Authors
Qing-Wen Wang ; Guihai Yu
Department of Mathematics, Shanghai University
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.
Keywords
Quaternion matrix equation; bisymmetric matrix; least-square solution; inertia
Main Subjects
15-XX Linear and multilinear algebra; matrix theory
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