The Core of a Grassmannian Frame

Let X={x_i}_i=1^m be a set of unit vectors in ℝ^n . The coherence of X is coh(X):=max _i≠j|⟨ x_i, x_j⟩ | . A vector x∈ X is said to be isolable if there are unit vectors x' arbitrarily close to x such that |⟨ x', y⟩ |n vectors for ℝ^n has the property that each vector in the core makes the angle α with a spanning family from the core. Consequently, the core consists of ≥ n+1 vectors. We then develop other properties of Grassmannian frames and of the core.