Uniqueness of the Eigenvalue Inverse Problem for a Class of X-type Matrices with Linear Relations

Abstract

Constraining a matrix by adding additional conditions to determine the matrix if given eigenpairs is called the eigenvalue inverse problem for matrices. The eigenvalue inverse problem of a matrix can be based on a given combination of different eigenvectors and real numbers to inverse a matrix method, and the method of inversion varies for different types of matrices. In this paper, we investigate the eigenvalue inverse problem for a class of X-type matrices characterized by linear relations, Invert the matrix based on its characteristics, determine eigenvalues and eigenvectors, and finally, prove that the solution of the problem exists and is unique, derive a series of expressions and recursive formulas, and we also check the algorithm’s accuracy correctness by giving different instances.