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Published on Apr 13, 2015
In Lecture 30 we introduced the Proj_W and Orth_W in terms of a given basis. Here I study these further and almost prove coordinate independence (in retrospect, there is a simple argument I'll show in a later post). We also see the matrix of the Proj is symmetric. I mentioned how you can use this to construct matrices with any old e-value you desire. Ultimately, 2 proofs of the theorem that W and W perp form the direct sum were given. We then applied the theorem to derive the normal equations for the least squares problem. We concluded with an overview of some inner products which were not dot-products and a brief discussion of Fourier series. Next up, the theory of adjoints and the spectral theorem.