# Computers in Scientific Discovery 6

21-25 August 2012
Portorož, Slovenia
UTC timezone
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# The rank of Hadamard powers of Euclidean distance matrices

Presented by Dr. Iztok KAVKLER
Type: Oral presentation

## Content

A matrix $A \in \mathbb{R}^{n \times n}$ is a Euclidean distance matrix (EDM) if there exist points $x_1, x_2, \dots, x_n \in \mathbb{R}^d$, such that $a_{ij} = ||x_i - x_j||^2$. The minimal possible $d$ is called the embedding dimension. A well known result states that the rank of an EDM is $d + 2$ for the points in a general position, and $d + 1$ if the points lie on a $d - 1$ dimensional hypersphere. In this talk, we extend the result to $k$-th Hadamard power of an EDM. The rank will be given in a closed form and is independent of the matrix size $n$, provided that $n$ is not too small. The result was obtained in the context of researching DNA descriptors for determining the degree of similarity of DNA sequences.

## Place

Location: Portorož, Slovenia
Address: University of Primorska, Faculty of Tourism Studies, Obala 11a, SI-6320 Portorož - Portorose, Slovenia
Room: VP1

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