The least-square bisymmetric solution to a quaternion matrix equation with applications

Document Type : Research Paper


Department of Mathematics, Shanghai University


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.


Main Subjects

  • Receive Date: 27 January 2011
  • Revise Date: 03 October 2011
  • Accept Date: 03 October 2011
  • First Publish Date: 15 May 2013