Advanced Linear Algebra

[!NOTE] This module explores the advanced elements of linear algebra, focusing on eigenvalues, eigenvectors, matrix decompositions, and their applications in dimensionality reduction and deep learning.

Welcome to Advanced Linear Algebra! This module covers the mathematical engine behind advanced machine learning techniques like Principal Component Analysis (PCA), Singular Value Decomposition (SVD), and deep neural networks.

1. Chapters

  1. Eigenvalues and Eigenvectors
    • Understand the core concepts of eigenvalues and eigenvectors.
    • Explore their geometric interpretations and importance in ML.
  2. Matrix Decompositions
    • Master Singular Value Decomposition (SVD) and Eigendecomposition.
    • Learn how to decompose complex matrices into simpler, interpretable parts.
  3. PCA and Dimensionality Reduction
    • Apply eigendecomposition to perform PCA.
    • Understand how to reduce feature dimensions while retaining variance.
  4. Tensors and Operations
    • Generalize vectors and matrices to N-dimensional tensors.
    • Explore tensor products, contraction, and broadcasting.
  5. The Jacobian and Hessian
    • Understand the Jacobian matrix for vector-valued functions.
    • Explore the Hessian matrix and its role in optimization.
  6. DL App: Neural Network Layers
    • See how advanced linear algebra powers deep learning layers.
    • Understand the math behind convolutional, recurrent, and attention layers.
  7. 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:

  • Compute and interpret eigenvalues and eigenvectors.
  • Perform SVD and Eigendecomposition on matrices.
  • Implement PCA for dimensionality reduction.
  • Work with N-dimensional tensors and understand their role in deep learning.

Module Chapters