Sorting vectors

Abstract

1. Introduction: In what follows, X will be a real inner-product linear space (inner product (x, y), norm |x| = (x, x)½); En will be n-dimensional real Euclidean space. We shall be dealing with sets {as: 1 ≤ s ≤ rk; r ≥ 1, k ≥ 2} of elements of X; we write a for the vector (a1; …, ark), and put . We suppose that |as| ≤ ∈ (< 0) for every s.