On the General Algebraic Inverse Eigenvalue Problems (Journal of Computational Mathematics, 2004)
A number of new results on sufficient conditions for the solvability and numerical algorithms of the following general algebraic inverse eigenvalue problem are obtained: Given $n+1$ real $n× n$ matrices $A=(a_{ij}),A_k=(a_{ij}^{(k)})(k=1,2,…,n)$ and $n$ distinct real numbers $λ_1,λ_2,…,λ_n,$ find $n$ real number $c_1,c_2,…,c_n$ such that the matrix $A(c)=A+\sum\limits_{k=1}^{n}c_k A_k$ has eigenvalues $λ_1,λ_2,…,λ_n.$
Keywords: Linear algebra; Eigenvalue problem; Inverse problem.