Re: Bilinear Forms

In article <1143825017.028094.26210@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
junoexpress <mathimagical@xxxxxxxxxxxx> wrote:

Let M be a nxn positive definite, Hermitian matrix
Let <*,*> denote complex inner product and |*| denote magnitude of a
complex number

Is the following statement true:
| <x,y> | <= |<x,z>| implies | <x,My> | <= |<x,Mz>| for all x,y,z
elements of C^n?



Can't you have a positive definite Hermitian matrix M
and three vectors with <x,y> = <x,z> = <x,Mz> = 0 and <x,My> = 1 ??
.