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pset 1 solutions

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Steven G. Johnson 2023-02-18 18:29:27 -05:00
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@ -115,7 +115,7 @@ The *nice* case of diagonalization is when you have **orthonormal eigenvectors**
* Uᵣ and Vᵣ as the "right" bases for C(A) and C(Aᵀ). Avₖ=σₖvₖ
* SVD and eigenvalues: U and V as eigenvectors of AAᵀ and AᵀA, respectively, and σₖ² as the positive eigenvalues.
* Deriving the SVD from eigenvalues: the key step is showing that AAᵀ and AᵀA share the same positive eigenvalues, and λₖ=σₖ², with eigenvectors related by a factor of A. From there you can work backwards to the SVD.
* pset 1 solutions: coming soon
* [pset 1 solutions](psets/pset1sol.ipynb)
* pset 2: coming soon
**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).

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