## 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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