## Direct sum and projection proof

Let W be subspace of a vector space V. Prove that if $V= W \bigoplus W^c.$ and T is orthogonal projection onto W, then T=T*.

$V= W \bigoplus W^c.$ is direct sum
$W^c$ is W complement
T* is T transpose conjugate.

I know:
$V= W \bigoplus W^c$ means
$v= w_1+w_2$, st $w_1 \in W_1$ and $w_2 \in W^c$
$T(w_1+w_2)= T(w_1)=w_1$

Not sure how to make T=T*?