Skip to main content

Subsection 2.1.2 Overview

  • 2.1 Opening Remarks

    • 2.1.1 Low rank approximation

    • 2.1.2 Overview

    • 2.1.3 What you will learn

  • 2.2 Orthogonal Vectors and Matrices

    • 2.2.1 Orthogonal vectors

    • 2.2.2 Component in the direction of a vector

    • 2.2.3 Orthonormal vectors and matrices

    • 2.2.4 Unitary matrices

    • 2.2.5 Examples of unitary matrices

    • 2.2.6 Change of orthonormal basis

    • 2.2.7 Why we love unitary matrices choice

  • 2.3 The Singular Value Decomposition

    • 2.3.1 The Singular Value Decomposition Theorem

    • 2.3.2 Geometric interpretation

    • 2.3.3 An "algorithm" for computing the SVD

    • 2.3.4 The Reduced Singular Value Decomposition

    • 2.3.5 The SVD of nonsingular matrices

    • 2.3.6 Best rank-k approximation

  • 2.4 Enrichments

    • 2.4.1 Principle Component Analysis (PCA)

  • 2.5 Wrap Up

    • 2.5.1 Additional homework

    • 2.5.2 Summary

login