Peter Bloem's PCA Introduction Series

It's one of the best linear algebra tutorial I've looked at
<http://peterbloem.nl/blog/pca>
PCA has similarities with Autoencoder
Minimizing reconstruction error == Maximizing variance (a^2 = b^2 + c^2)
- Best fit == Perpendicular Projection
- Combined (not unique) solution v.s. greedy iterative solution
Ortho-normal matrix is a rotation/flipping-only transformation
- Data normalization and basis transformations
The great human-face dataset example
Spectrum theory
We then looked at eigenvectors, and we show that the eigenvectors of the data covariance 𝐒 arise naturally when we imagine that our data was originally decorrelated with unit variance in all directions. To me, this provides some intuition for why PCA works so well when it does. We can imagine that our data was constructed by sampling independent latent variables 𝐳 and then mixing them up linearly.
SVD
Part 3 - Proof of the Spectrum Theorem
Determinant - Inflation
this reminds me of the 理解相对论
<https://www.bilibili.com/video/BV17P4y1V7BX?from=search&seid=11798032574058936658&spm_id_from=333.337.0.0>
Non-trivial Null Space of $ | A - \lambda I | $
Complex Number and Multiplication

Part 3 - Proof of the Spectrum Theorem