Normed vector space

Equivalence of norms

Given a vector space , two norms are said to be equivalent iff there exist such that

for all . #m/def/linalg This defines an Equivalence relation on norms.

Properties

• All norms on a finite dimensional space are equivalent
• Norms are equivalent iff they induce the same topology.

#state/tidy | #lang/en | #SemBr