A Hermitian inner product $\langle\cdot,\cdot\rangle$ on a complex vector space $V$ is a bilinear form on $V$ that is antilinear in the second slot. That is,
- $\langle u+v,w\rangle = \langle u,w\rangle +\langle v,w\rangle$;
- $\langle u,v+w\rangle = \langle u,v\rangle +\langle u,w\rangle$;
- $\langle \alpha u ,v\rangle = \alpha\langle u,v\rangle$ ;
- $\langle u ,\alpha v\rangle = \overline\alpha\langle u,v\rangle$ ;
- $\langle u,v\rangle = \overline{\langle v,u\rangle}$
- $\langle u,u \rangle \geq 0$
- $\langle u,u \rangle = 0$ if and only if $u=0$.
Wikidata ID: Q77583424