Computational Information Geometry Wonderland

I am teaching the fundamentals of 3D at Ecole Polytechnique (INF555). We are currently looking at various matrix decompositions and their use in visual computing.

To compute the PCA of high-dim datasets, we just need to compute the SVD of the covariance matrix of zero-mean normalized data sets. So I looked for a good source of explanations of SVD and I came across the lecture of Gilles Strang:
SVD lecture

Here, the 4 subspaces (image and nullspace) of column/row matrices are reviewed and it is shown how to compute the SVD by simply solving left/right eigenproblems.

Definitively worth watching! (you'll see on one example a problem with the sign in a SVD decomposition to solve!!!)