Normed Vector Space 2.14 2001/12/31 2005/10/04 10:10:10.599 GMT-5 Phil Schniter schniter@ee.eng.ohio-state.edu Elizabeth Chan lizychan@rice.edu Phil Schniter schniter@ee.eng.ohio-state.edu normed vector space This module introduces normed vector space. Now we equip a vector space V with a notion of "size". A norm is a function ( : ⋅ V ) such that the following properties hold ( x y x V y V and α α  ): x 0 with equality iff x 0 α x α ⋅ x x y x y , (the triangle inequality). In simple terms, the norm measures the size of a vector. Adding the norm operation to a vector space yields a normed vector space. Important example include: V N , ≔ x 0 … x N - 1 i 0 N 1 x i 2 x x V N , ≔ x 0 … x N - 1 i 0 N 1 x i 2 x x V l p , ≔ x n n x n p 1 p V ℒ p , ≔ f t t f t p 1 p