Left and right inverse eigenpairs problem for -hermitian matrices and its optimal approximate problem are considered. Based on the special properties of -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.
"Left and Right Inverse Eigenpairs Problem for -Hermitian Matrices." J. Appl. Math. 2013 (SI03) 1 - 6, 2013. https://doi.org/10.1155/2013/230408