Invariance of the norm by permutations
Solution 1:
No. For example $\Vert(x,y)\Vert = |x| + 2 |y|$ defines a norm on $\mathbb{R}^2$.
Invariance of the norm by permutations
Solution 1:
No. For example $\Vert(x,y)\Vert = |x| + 2 |y|$ defines a norm on $\mathbb{R}^2$.