Eigenvalue inverse the problem with generalized arrow matrices with linear relations

Abstract The inverse problem of eigenvalues of matrices is nowadays a popular topic in numerical algebra and is widely used in mathematical physics inverse problems. This paper studies the eigenvalue inverse of generalized arrow matrices with linear relations, in which the concept of an eigenpair is used and the existence and unambiguousness of the solution of the equation generated by the problem are shown. Recursive expressions are given according to the laws. The validity of the algorithm will be verified with exact conditions. Finally, the conclusion is drawn.