A matrix inverse eigenvalue problem and its application
type: Item
instance of: scholarly article
title: A matrix inverse eigenvalue problem and its application
zbMATH Open document ID: 0901.15003
DOI: 10.1016/S0024-3795(96)00639-8
author: Nian Li
published in: Linear Algebra and its Applications
publication date: 1998-11-15T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 93B55
Mathematics Subject Classification ID: 92B20
zbMATH DE Number: 1083214
zbMATH Keywords: inverse eigenvalue problem
zbMATH Keywords: spectrum
zbMATH Keywords: algorithm
zbMATH Keywords: pole assignment
zbMATH Keywords: neural networks
reviewed by: Erwin O. Kreyszig
MaRDI profile type: Publication
cites work: Approaches to robust pole assignment
cites work: Q3359644
cites work: Matrix Analysis
cites work: Robust pole assignment in linear state feedback
cites work: Designing the Hopfield neural network via pole assignment
cites work: Q5674306
cites work: Geometric state-space theory in linear multivariable control: A status report
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description: scientific article; zbMATH DE number 1083214