Inverse eigenproblem of anti-symmetric and persymmetric matrices and its approximation
Dongxiu Xie, Yanping Sheng · Inverse Problems · 2003
The problem of generating a matrix A with specified eigenpair, where A is an anti-symmetric and persymmetric matrix, is presented. The solvability conditions are studied. A general expression of such a matrix is provided. We denote the set of such matrices by E n . The best approximation problem associated with E n is discussed, that is: to find the nearest matrix to a given matrix A * by A ∊ E n . The existence and uniqueness of the best approximation problem is proved and the expression of this nearest matrix is provided.