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lecture 8 demos

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@ -120,11 +120,16 @@ The *nice* case of diagonalization is when you have **orthonormal eigenvectors**
**Further reading**: [OCW lecture 6](https://ocw.mit.edu/courses/18-065-matrix-methods-in-data-analysis-signal-processing-and-machine-learning-spring-2018/resources/lecture-6-singular-value-decomposition-svd/) and textbook section I.8. The [Wikipedia SVD article](https://en.wikipedia.org/wiki/Singular_value_decomposition).
## Lecture 6 (Feb 21)
## Lecture 7 (Feb 21)
* [SVD demo with image "compression"](https://nbviewer.org/github/mitmath/1806/blob/fall22/notes/SVD-intro.ipynb)
* [Low-rank approximation](https://en.wikipedia.org/wiki/Low-rank_approximation) and the Eckart–Young theorem.
* Vector [norms](https://en.wikipedia.org/wiki/Norm_(mathematics)) (ℓ², ℓ¹, and ℓ∞) and [Matrix norms](https://en.wikipedia.org/wiki/Matrix_norm). Unitarily invariant norms, and unitary invariance of singular values.
* [Matrix completion], the ["Netflix problem"](https://en.wikipedia.org/wiki/Netflix_Prize), and the nuclear norm.
**Further reading**: Textbook sections I.9, I.11, III.5. [OCW lecture 7](https://ocw.mit.edu/courses/18-065-matrix-methods-in-data-analysis-signal-processing-and-machine-learning-spring-2018/resources/lecture-7-eckart-young-the-closest-rank-k-matrix-to-a/) and [lecture 8](https://ocw.mit.edu/courses/18-065-matrix-methods-in-data-analysis-signal-processing-and-machine-learning-spring-2018/resources/lecture-8-norms-of-vectors-and-matrices/).
**Further reading**: Textbook sections I.9, I.11, III.5. [OCW lecture 7](https://ocw.mit.edu/courses/18-065-matrix-methods-in-data-analysis-signal-processing-and-machine-learning-spring-2018/resources/lecture-7-eckart-young-the-closest-rank-k-matrix-to-a/) and [lecture 8](https://ocw.mit.edu/courses/18-065-matrix-methods-in-data-analysis-signal-processing-and-machine-learning-spring-2018/resources/lecture-8-norms-of-vectors-and-matrices/).
## Lecture 8 (Feb 22)
* [PCA demo](https://nbviewer.org/github/mitmath/1806/blob/fall22/notes/Statistics-and-PCA.ipynb)
* [Least-squares demo](https://nbviewer.org/github/mitmath/1806/blob/fall22/notes/Least-Square%20Fitting.ipynb)