Show that $\|.\|_{1/2}$ is not a norm.

Question

Show that $\|.\|_{1/2}$ is not a norm. would anybody guide me that how can i prove or disprove?

thanks

Answer 1

It doesn't satisfy the triangle inequality. All you need is a counter-example to show it isn't a norm. For example in $\mathbb R^2$ consider $(1,0)$ and $(0,1)$.