Singular Value Decomposition (SVD)

Singular Value Decomposition (SVD)#

About the project#

  • Duration: 3–4 hours in class, 1–2 hours preparation at home

  • Prerequisites: Linear algebra (orthonormal bases, dot products, eigenvalues/eigenvectors at a conceptual level, matrix–vector and matrix–matrix multiplication), calculus basics for continuity/IVT intuition (Bolzano/Intermediate Value Theorem), basic numerical methods intuition (root finding / solving nonlinear systems), and basic programming (NumPy arrays, functions, loops, plotting, simple interactivity)

  • Python packages: numpy, matplotlib, scipy (root finding / nonlinear solving), ipywidgets (interactive sliders), PIL (image handling)

  • Learning objectives: Understand and apply the SVD theorem \(A=U\Sigma V^T\) and the meaning of singular values/vectors; derive and interpret SVD geometrically for full-rank \(2\times2\) matrices via unit circle → ellipse; implement interactive visualizations to identify orthogonal*

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