# Math Help - more Adjoint of Linear operator confusion...

1. ## more Adjoint of Linear operator confusion...

So I have to prove the following, and not sure where to go with it:
Prove that if $V=W\oplus W^{\perp}$ and T is the projection on W along $W^{\perp}$ then T=T*.
Any help? THanks

2. Originally Posted by dannyboycurtis
So I have to prove the following, and not sure where to go with it:
Prove that if $V=W\oplus W^{\perp}$ and T is the projection on W along $W^{\perp}$ then T=T*.
Any help? THanks
let $v_1=w_1+w_1', \ v_2=w_2+w_2'$ where $w_i \in W, \ w_i' \in W^{\perp}.$ then $==$ and $==.$

so $=$ and thus $T=T^*.$