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Czechoslovak Mathematical Journal, Vol. 69, No. 4, pp. 1015-1027, 2019

Inverse eigenvalue problem of cell matrices

Sreyaun Khim, Kijti Rodtes

Received December 20, 2017.   Published online February 22, 2019.
Abstract:  We consider the problem of reconstructing an $n \times n$ cell matrix $D(\vec{x})$ constructed from a vector $\vec{x} = (x_1, x_2,\dots, x_n)$ of positive real numbers, from a given set of spectral data. In addition, we show that the spectra of cell matrices $D(\vec{x})$ and $D(\pi(\vec{x}))$ are the same for every permutation $\pi\in S_n$.
Keywords:  cell matrix; inverse eigenvalue problem; Euclidean distance matrix
Classification MSC:  15B10, 15B05, 15B48, 35P30, 35P20
DOI:  10.21136/CMJ.2019.0579-17
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Affiliations:   Sreyaun Khim, Department of Mathematics, Faculty of Science, Naresuan University, 99 Moo 9 Phitsanulok-Nakhonsawan Road Tambon Tapho, Muang, Phitsanulok 65000, Thailand, e-mail: sreyaun.khim@yahoo.com; Kijti Rodtes, Department of Mathematics, Faculty of Science, Naresuan University, Research Center for Academic Excellence in Mathematics, 99 Moo 9 Phitsanulok-Nakhonsawan Road Tambon Tapho, Muang, Phitsanulok 65000, Thailand, e-mail: kijtir@nu.ac.th
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