Question

Does the norm function* satisfy: \(f(\alpha x) = \alpha f(x)\), where \(\alpha\) is an arbitrary scalar; \(\alpha\in\mathbb R\)?

* 2-norm vector function
\[\text{2-norm}(x) \equiv \|x\|_2 \triangleq \sqrt{x\cdot x}\]

Answer 1

No.

Answer 2

Only for positive alpha?

Answer 3

youse've got it