I saw the statement "Given two subspaces $\mathbf{V}_1$, $\mathbf{V}_2 \subseteq \Re^d$, then the canonical angles between the subspaces $\mathbf{V}_1$ and $\mathbf{V}_2$ is given by the singular values of $\mathbf{V}_1'\mathbf{V}_2$.
Where can I find the proof for the above ?.
I am sorry that my comment wasn't too helpful. You will find a full proof in Numerical Methods for Computing Angles Between Linear Subspaces by Björck and Golub. It is available here. The statement you are searching for is Theorem 1 of section 3. I also recommend to read the short introduction to this section. I hope this helps you and sufficiently answers your question.