A passive transformation is instead an endomorphism on K n . This is applied to the components: v i ↦ ↦ T i j v j =: v i ′ . Provided that T is invertible, the new basis B ′ = { e i ′ } is determined by asking that v i e i = v i ′ e i ′ , from which the expression e i ′ = ( T − − 1 ) j i e j can be derived.