# Math Help - inner product space question

1. ## inner product space question

I have a question.
If T is a linear operator on an inner product space, say V, and W is a T-invariant subspace of V, how could I show that $W^{\perp}$ is T*-invariant, where T* is the adjoint of T.

2. Originally Posted by dannyboycurtis
I have a question.
If T is a linear operator on an inner product space, say V, and W is a T-invariant subspace of V, how could I show that $W^{\perp}$ is T*-invariant, where T* is the adjoint of T.

For $w'\in W^\perp$ we get:

$T^{*}w'\in W^\perp\Longleftrightarrow =0\,\,\,\forall w\in W\Longleftrightarrow$ $=0\,\,\,\forall w\in W$...but this last equality is true....

Tonio