Fix a finite-dimensional vector space V over a field K (thought of as R or C ), and a basis B = { e i } 1 ≤ ≤ i ≤ ≤ n of V . This basis provides an isomorphism C : K n → → V via the component map ( v i ) 1 ≤ ≤ i ≤ ≤ n = ( v 1 , ⋯ ⋯ , v n ) ↦ ↦ ∑ ∑ i v i e i .