Image processing: using PCA for 3d object recognition
Principle Component Analysis by itself is not going to provide rotational or scale invariance. You still have to provide templates for rotational and scaled models for image/template matching. What PCA does do is reduce the dimensionality of the search space  by converting a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components.

Now since number of principle components &lt;= number of components, you save on the search space.

What the lecture tries to tell you is with the eigenvectors, you get an efficient representation of the scales of the template which are easier to manipulate(a single scale factor) then manipulating the entire image everytime.