Linear Algebra — Interactive Explainers
Six standalone, fully offline visualizers accompanying the Linear Algebra module. Each opens in any browser with a double-click — no internet, no installation. Drag, click, and slide; every number on screen is computed live from the same formulas derived in lecture.
ℓp Unit Balls
Slide p and watch the unit ball morph from diamond (ℓ₁) through circle (ℓ₂) to square (ℓ∞). See why ℓ₁ corners produce sparsity, and what breaks when p < 1.
Open → Explainer 2Cosine Similarity
Drag two vectors and read xᵀy, the angle, and cos θ live. Presets for aligned, orthogonal, and opposite pairs — the geometry behind embeddings and retrieval.
Open → Explainer 3Least Squares Line Fitting
Click to add points; the OLS line, residuals, and the live XᵀX, Xᵀy, β̂ panels update instantly. Presets show the R² trap and how one outlier swings the fit.
Open → Explainer 4Eigenvectors as Fixed Directions
Drag v and watch Av. On the eigen-lines, Av stays put — off them, it rotates away. Edit the matrix, try shear and rotation, and run power iteration to find the dominant eigenvector.
Open → Explainer 5Rotate · Scale · Rotate
Animate A = UΛUᵀ step by step: the unit circle rotates into the eigen-frame, stretches along the axes, and rotates back into a tilted ellipse. The spectral theorem, in motion.
Open → Explainer 6PCA Playground
Click to build a dataset; the covariance matrix, eigenvalues, principal components, and explained-variance bars react live. Toggle projections and reconstruction to see what 1-D keeps and loses.
Open →