On properties of cell matrices

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.

• Type: Journal
• Year: 2010
• Where: AMC
• Authors: Gasper Jaklic, Jolanda Modic
• Keywords: AMC 2010, Cell Matrices, K-cell Matrices, Polynomial Lagrange Interpolation