A collection of concept problems applying linear algebra — matrix singularity, rank, eigenvalues, PCA, and more — to real machine learning scenarios. Each problem is grounded in situations you'll commonly encounter in actual ML pipelines.
A hands-on coding practice for implementing matrix operations, Gaussian elimination, eigendecomposition, and PCA from scratch using NumPy. Each problem includes step-by-step hints and complete solution code.
Wrap up the core of linear algebra: geometric interpretation of determinants, basis and span, eigenvalue/eigenvector computation, how PCA works under the hood with full derivations, and Markov matrices.
A comprehensive guide to vector norms, dot products, scalar multiplication, the concept of linear transformations, matrix multiplication, inverse matrix computation, and how all these ideas connect in neural networks (the perceptron).
A clear walkthrough of solving linear systems via elimination, computing Row Echelon Form (REF) and Reduced Row Echelon Form (RREF) through Gaussian elimination, and using Rank to determine the number of solutions.
A walkthrough of how systems of linear equations are used in machine learning — covering singular vs. non-singular matrices, linear independence/dependence, and determinant calculation.