Week of 1/21/08

Definition of complex (Hermitian) inner product

< u + v,w > = = < u,w > + < v,w >

< u,v + w > = = < u,v > + < u,w >

< αu,v > = = α < u,v >

< u,αv > = = α ^* < u,v >

< u,v > = = < v,u > ^*

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

The basic example is the form

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