Left and Right Inverse Eigenpairs Problem for κ -Hermitian Matrices

Abstract

Left and right inverse eigenpairs problem for $\kappa$-hermitian matrices and its optimal approximate problem are considered. Based on the special properties of $\kappa$-hermitian matrices, the equivalent problem is obtained. Combining a new inner product of matrices, the necessary and sufficient conditions for the solvability of the problem and its general solutions are derived. Furthermore, the optimal approximate solution and a calculation procedure to obtain the optimal approximate solution are provided.