In a normed vector space show that the union of any class of op... | Filo

Vector Space Definition, Axioms & Examples

Problems1. Show that the norm x of x is the distance from x to 0 .2. Verify that the usual length of a vector in the plane or in three dimensional space has properties (a), (b) and (c) of a norm.3. Show that for any element x of a normed linear space x≥ 0 follows from axioms (b) and (c) of a normed linear space.4. Given x={ξi}⊂ℝ^n, show that x=(∑i=1^n|ξi|^2)^1 / 2 defines a norm on ℝ^n.

Basis of a Vector Space | Definition & Examples