On properties of cell matrices |
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| Authors: | Gašper Jakli? Jolanda Modic |
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| Institution: | a FMF and IMFM, University of Ljubljana and PINT, University of Primorska, Jadranska 21, 1000 Ljubljana, Slovenia
b FMF, University of Ljubljana, Jadranska 21, 1000 Ljubljana, Slovenia |
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| Abstract: | In this paper properties of cell matrices are studied. A determinant of such a matrix is given in a closed form. In the proof a general method for determining a determinant of a symbolic matrix with polynomial entries, based on multivariate polynomial Lagrange interpolation, is outlined. It is shown that a cell matrix of size n>1 has exactly one positive eigenvalue. Using this result it is proven that cell matrices are (Circum-)Euclidean Distance Matrices ((C)EDM), and their generalization, k-cell matrices, are CEDM under certain natural restrictions. A characterization of k-cell matrices is outlined. |
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| Keywords: | Cell matrix Star graph Determinant Eigenvalues Euclidean distance matrix Circum-Euclidean distance matrix |
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