Linear Algebra Basics

[!NOTE] This module explores the foundational elements of linear algebra, translating mathematical concepts into concrete code and data structures used in machine learning.

Welcome to Linear Algebra Basics! This module is the starting point for understanding how data is represented and manipulated in Machine Learning models.

1. Chapters

  1. Scalars, Vectors, and Matrices
    • Learn the basic building blocks of linear algebra.
    • Understand dimensions, shapes, and the leap from math to code.
  2. Vector and Matrix Operations
    • Explore addition, scalar multiplication, and broadcasting.
    • Master the dot product and understand cosine similarity.
  3. Matrix Multiplication
    • Go deep into the core operation of neural networks.
    • Understand linear transformations and matrix-vector products.
  4. Systems of Equations
    • Solve systems of equations using matrices.
    • Explore the concepts of span, linear independence, and rank.
  5. ML Application: Data Vectors
    • Apply your knowledge to represent data as vectors.
    • Understand embeddings and how algorithms process text and images.
  6. Module Review: Flashcards & Cheat Sheet
    • Review key concepts and formulas.
    • Test your knowledge with interactive flashcards.

2. Learning Goals

By the end of this module, you will be able to:

  • Identify and define scalars, vectors, matrices, and tensors.
  • Perform basic operations and interpret their geometric meaning.
  • Compute matrix products and understand them as linear transformations.
  • Represent real-world datasets as matrices and vectors for ML models.

Module Chapters