Abdo Alfakih, University of Windsor

Abstract

An n-by-n matrix D is a Euclidean distance matrix (EDM) if its entries can be realized as the interpoint squared Euclidean distances of an n-point configuration. If the points of the configuration lie on a sphere of radius ρ, then the corresponding EDM is said to be spherical of radius ρ.

In the first part of this talk, I will survey the basic theory of EDMs, where the main emphasis will be on various properties and characterizations of EDMs and spherical EDMs. In the second part, I will discuss recently obtained results on a couple of distance geometry problems posed in terms of EDMs. The following is an example of such problems. Given a spherical EDM D of unit radius and 1≤ k < l ≤ n, characterize the set of all spherical EDMs of unit radius whose entries agree with those of D except possibly with the entry in the klth and lkth positions.

Video