Thread: Inner product space proof question

Let T be a linear operator on a complex inner product space V.
How to prove that T is Hermitian if and only if <T(x),x> is real for all x in V.

Dont really have any idea how to start.

Any help would be appreciated.

Thanks in advance.

Originally Posted by firebio

Let T be a linear operator on a complex inner product space V.
How to prove that T is Hermitian if and only if <T(x),x> is real for all x in V.

Dont really have any idea how to start.

Any help would be appreciated.

Thanks in advance.

; but in

general, , so:

is Hermitian ... end the argument.

Tonio