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A matrix inverse eigenvalue problem and its application. (English) Zbl 0901.15003

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.

MSC:

15A18 Eigenvalues, singular values, and eigenvectors
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
93B55 Pole and zero placement problems
92B20 Neural networks for/in biological studies, artificial life and related topics
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References:

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