EDB — 0ZV

[0ZV] A norm is an operation that maps a vector \(v∈ X\) in a real number \(\| v\| \), which satisfies

1. \(\| v\| ≥ 0\) and \(\| v\| =0\) if and only if \(v=0\);

2. for every \(v∈ X\) and \(t∈ {\mathbb {R}}\) we have \(|t|\, \| v\| =\| tv\| \) (we will say that the norm is absolutely homogeneous);

3. (Triangle inequality) for every \(v,w∈ X\) we have

   \[ \| v+w\| ≤ \| v\| +\| w\| \quad ; \]

   this says that one side of a triangle is less than the sum of the other two.