- Every machine learning model relies on three pillars: linear algebra, calculus, and convex optimization.
- The MNIST dataset is treated as a matrix of 70,000 rows (images) and 784 columns (pixels) after flattening.
- Data exploration shows balanced classes, no missing values, and a bimodal pixel intensity distribution.
- Vectors have L1 and L2 norms; dot products measure similarity between images.
- Matrix multiplication forms a Gram matrix of pairwise similarities.
- Broadcasting allows adding a scalar bias to tensors without explicit loops.
- Projections decompose images into components along and perpendicular to the mean image direction.
- The Singular Value Decomposition (SVD) factors the centered data matrix and reveals 626 significant singular values out of 784.