I'm unable to do the following problem : Let be a vector space over whose dimension is and with an inner product . Let be a subspace of with dimension and be an orthonormal basis of .
We define the orthogonal projection over as .
Demonstrate that , .
My attempt : I suppose it's true and want to see that it's really true ( don't want to fall over any contradiction).
So . And I didn't reach anything.
Thank you very much Jose. I'll think about it tomorrow. To tell you the truth I was so tired when I posted my thread that I actually didn't think a lot but rather used my short term memory to post what I did today.
I need a rest. My exam is on Monday so I'm pushing hard!