0
$\begingroup$

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 $p(0) = 0$

  • 0
    I believe in (2), it should be absolute value of $\alpha$ instead of norm of $\alpha$. Anyway, picking $\alpha = 0$ answers the question.2012-08-16

1 Answers 1

1

Look at property (2), and use the fact that $0\cdot x = 0$ for any vector $x$.