The Inverse Generalized Eigenvalue Problem for Generalized Centro-anti-symmetric Matrices

Given matrix X, Lambda, find the generalized centro-anti-symmetric matrices solutions A, B of inverse generalized eigenvalue problem AX = BX Lambda. The general expression of solution to the problem is provided. The set of such solutions is denoted by S-[A,S-B]. The optimal approximation problem associated with S-[A,S-B] is posed, that is: to find the nearest triple matrix [A,B] from S-[A,S-B]. The existence and uniqueness of the optimal approximation problem is discussed and the expression is provided for the nearest triple matrix.