The Inverse Eigenvalue Problem of Generalized Reflexive Matrices

A real symmetric unipotent matrix P is said to be generalized reflection matrix. A real matrix A is said to be a generalized reflexive matrix with respect to generalized reflection matrix dual (P,Q) if A = PAQ. This paper involves related inverse eigenvalue problems of generalized reflexive matrices and their optimal approximation. Necessary and sufficient conditions for the solvability of the problem are derived,the general expression of the solution is given. The optimal approximate solution is also provided.

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