The solvability conditions for inverse eigenproblem of symmetric and anti‐persymmetric matrices and its approximation
Dongxiu Xie, Xi-Yan Hu, Lei Zhang · Numerical Linear Algebra with Applications · 2002
Abstract The problem of generating a matrix A with specified eigen‐pair, where A is a symmetric and anti‐persymmetric matrix, is presented. An existence theorem is given and proved. A general expression of such a matrix is provided. We denote the set of such matrices by 𝒮𝒜𝒮 E n . The optimal approximation problem associated with 𝒮𝒜𝒮 E n is discussed, that is: to find the nearest matrix to a given matrix A * by A ∈𝒮𝒜𝒮 E n . The existence and uniqueness of the optimal approximation problem is proved and the expression is provided for this nearest matrix. Copyright © 2002 John Wiley & Sons, Ltd.