Dual Spaces

Abstract

Definition 1 (Dual Space) Let V be a finite dimensional vector space. (a) A linear functional on V is a function u * : V → IR that is linear in the sense that u * (v + w) = u * (v) + u * (w) and u * (α v) = α u * (v) for all u, w ∈ V and all α ∈ IR.