For uni I've got this exercise where i need to prove the following:
$$\sigma_{max}(X^\dagger)^2 \ ||Xw-Xw^* ||_2^2 \geq ||w - w^* ||_2^2$$
where $\sigma_{max}(A) = max_{u \in \mathbb{R}^d \ ||u||_2 = 1} ||Au||_2$ is the largest singular value for matrix $A$, and $X^\dagger$ is the pseudo-inverse of matrix $X$.
I've tried just writing out the left hand side, but this did not help me any further. Does anyone know how I could tackle this problem? Thanks in advance!!