In my math course about Linear Regression the following is stated:

We know from linear algebra that the function
g(t) = (MT Mt,t)

attends its minimum on the unit sphere at a point, which is the eigenvector corresponding tot the smallest eigenvalue of the matrix MT M.
Could anyone give me a clue of where to find more information or proof of this?

(T stands for Transpose, I can't find a way to add a superscript.)