$$\|u\| = 1$$ let $\hat{X_j}$ be the projected vector correspond to the span of $u$, and that $\hat{X_j} = uu^TX_j$. The projection matrix $uu^T$ is
1) $(uu^T)^T = uu^T$.
2) $(uu^T)(uu^T) = uu^T$.
I have two questions.
Q1 . Since $uu^T=\langle u, u\rangle = \|u\|$, should this equal to $1$?
Q2 . How come $u^Tu=1?$