A matrix inverse eigenvalue problem and its application
For given real \(n\)-vectors \(x_1, \dots, x_p\), \(y_1, \dots, y_p\) and complex \(S= \{\lambda_1, \dots, \lambda_n\}\) find a real \(n\times n\) matrix \(A\) such that \(Ax_j =y_j\), \(j=1, \dots, p\), and \(S\) is the spectrum of \(A\). The paper proves an existence theorem and an algorithm for \(A\) and relates the problem to the pole assignment problem of control theory and to designing neural networks.
scientific article; zbMATH DE number 1083214
scientific article