Module 5 Overview

Module 5 — Linear Algebra & Random

Welcome

This module covers two pillars of scientific computing with NumPy: linear algebra (vectors, matrices, and the equations that relate them) and random number generation (sampling, simulation, and reproducibility). Together they’re the backbone of everything from graphics to machine learning to Monte Carlo simulation — which is exactly where this module ends up.

Learning goals

• Compute dot products, norms, and cosine similarity between vectors
• Multiply matrices with @ and know how it differs from elementwise *
• Solve linear systems with np.linalg.solve instead of inverting matrices by hand
• Find eigenvalues/eigenvectors and verify them directly from their definition
• Generate reproducible random numbers with the modern Generator API
• Combine random sampling with vectorized boolean indexing to run a simulation

Setup — run this first.