I am reading about seminorm in vectorial spaces. Basically a norm $p$ have below properties:
1)$p(x+y) \leq p(x) + p(y)$;
2)$p(\alpha x) = \Vert \alpha\Vert p(x)$
Demonstrate that $p(0) = 0$
I am reading about seminorm in vectorial spaces. Basically a norm $p$ have below properties:
1)$p(x+y) \leq p(x) + p(y)$;
2)$p(\alpha x) = \Vert \alpha\Vert p(x)$
Demonstrate that $p(0) = 0$
Look at property (2), and use the fact that $0\cdot x = 0$ for any vector $x$.