Frame Potentials and Orthogonal Vectors

Abstract

An extension is given of a recent result of Glazyrin, showing that an orthonormal basis {ei} d i=1 joined with the vectors {ej} m j=1 , where 1 ≤ m < d minimizes the p-frame potential for p ∈ [1, 2 log 2m+1 2m / log m+1 m ] over all collections of N = d + m vectors {x1, . . . , xN } in S d−1 .