The inverse eigenvalue problem of structured matrices from the design of Hopfield neural networks

Lei Zhu and Wei-wei Xu

Applied Mathematics and Computation, 2016, vol. 273, issue C, 1-7

Abstract: By means of the properties of structured matrices from the design of Hopfield neural networks, we establish the necessary and sufficient conditions for the solvability of the inverse eigenvalue problem AX=XΛ in structured matrix set SARJn. In the case where AX=XΛ is solvable in SARJn, we derive the generalized representation of the solutions. In addition, in corresponding solution set of the equation, we provide the explicit expression of the nearest matrix to a given matrix in the Frobenius norm.

Keywords: Structured matrix; Inverse eigenvalue problem; Matrix norm; Optimal approximation; Frobenius norm (search for similar items in EconPapers)
Date: 2016
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:273:y:2016:i:c:p:1-7

DOI: 10.1016/j.amc.2015.08.089

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