TITLE: Almost complex structure which fails to be compatible
QUESTION [5 upvotes]: Let $V$ be a real vector space equipped with a scalar product $\langle, \rangle$ (i.e. a positive definite symmetric bilinear form). 
We say that an endomorphism $J: V \to V$ is an almost complex structure if $J^2=-Id.$ 
$J$ is said to be compatible with the scalar product if $\langle J v, J w \rangle = \langle v, w \rangle. $
I'd like a very simple example of a scalar product and almost complex structure such that $J$ FAILS to be compatible with $\langle, \rangle.$   This is very basic -and hopefully trivial- but I can't find any counterexamples.

REPLY [12 votes]: Take $\mathbb R^2$ with standard scalar product and $J(x,y)=(2y,-\frac12x)$.