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 $\displaystyle W^{\perp}$ is T*-invariant, where T* is the adjoint of T.
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 $\displaystyle W^{\perp}$ is T*-invariant, where T* is the adjoint of T.
For $\displaystyle w'\in W^\perp$ we get:
$\displaystyle T^{*}w'\in W^\perp\Longleftrightarrow <w,T^{*}w'>=0\,\,\,\forall w\in W\Longleftrightarrow$ $\displaystyle <Tw,w'>=0\,\,\,\forall w\in W$...but this last equality is true....