Week of 1/21/08

Definition of complex (Hermitian) inner product

$\langle u+v,w \rangle \equiv <u,w>+<v,w>$

$<u,v+w> \equiv <u,v>+<u,w>$

$<\alpha u,v> \equiv \alpha<u,v>$

$<u,\alpha v> \equiv \alpha^* <u,v>$

$<u,v> \equiv <v,u> ^*$

< u,u > > = 0, with equality only if u = = 0

The basic example is the form

$h(z,w) \equiv \sum z_i w^* _i$