Seminorm - Axioms of Choice

Processing math: 100%

Seminorm

Set

context	$F$ … subfield of $\mathbb{C}$
context	$V$ … $F$ -vector space
definiendum	$p\in \mathrm{SemiNorm}(V)$
postulate	$p:V\to \mathbb R$
$v,w\in V$
postulate	$p(v+w) \le p(v)+p(w)$
$\lambda\in F$
postulate	$p(\lambda\cdot v) = \|\lambda\|\cdot p(v)$

Discussion

A Norm is a seminorm with the adition axiom

$p(v)=0 \implies v=0$

(which I also write as $p(!0)=0$ .)

Reference

Wikipedia: Norm

Parents

Context

Log In

Improvements of the human condition