Introduction

Advanced Linear Algebra in Python

Linear algebra is the backbone of machine learning, scientific computing, and engineering. This course takes you beyond the basics — from orthogonal projections to eigenvalue algorithms — implementing each idea in pure Python from scratch.

You will build:

  • QR decomposition via Gram-Schmidt — the numerically stable way to factor any matrix
  • LU and Cholesky decompositions — the workhorses of direct linear solvers
  • Power iteration and deflation — extracting eigenvalues one by one
  • The pseudoinverse — solving underdetermined and overdetermined systems
  • PCA — finding the directions of maximum variance in data
  • The matrix exponential — bridging linear algebra and differential equations
  • Conjugate Gradient — the iterative solver behind large-scale machine learning

All implementations use only Python's standard math module — no NumPy, no shortcuts. When you finish, you will understand exactly what those library functions do under the hood.

Next →