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N.B.: The deck isn't completely standalone since I don't explain every step made as I did when actually presenting it. That said I think the deck should be useful for anyone who wants to get a quick idea of what PCA is and the math behind it (I only take into account conventional PCA, not probabilistic interpretations). I am inconsistent with some of my equations to make some of the algebra easier (all legal though!) which I explained during the actual presentation. For people who want to go deeper and follow the math more closely I highly recommend the tutorial by Jonathan Shlens which is where I got most of my derivations.
See the last slide of the deck for additional resources.