Negative of a power of a norm. I have one silly doubt if $\|.\|$ is a norm on a Hilbert space, then is it correct that $$\|x\|^{\mu} = \|-x\|^{\mu}, \qquad \mu \in (0, 1)$$
Please help me to understand the above concept.
According to me, it must be correct as $\|\alpha x \| = |\alpha|\|x\|$, for any scaler $\alpha$. 


We have for a norm $\|.\|$ in a Hilbert-space and $\mu\in(0,1)$
  \begin{align*}
 \color{blue}{\|-x\|^{\mu}}=\|(-1)\cdot x\|^{\mu}=\left(|-1|\|x\|\right)^{\mu}=\color{blue}{\|x\|^{\mu}}
\end{align*}

