Linear Algebra for Machine Learning

Essential linear algebra concepts and their applications in machine learning

Core Concepts

1. Vectors and Matrices

  • Vector operations (addition, multiplication, dot product)
  • Matrix operations (addition, multiplication, transpose)
  • Special matrices (identity, diagonal, symmetric)
  • Applications in feature representation and transformations

2. Linear Transformations

  • Matrix transformations
  • Eigenvalues and eigenvectors
  • Singular Value Decomposition (SVD)
  • Applications in dimensionality reduction (PCA)

3. Vector Spaces

  • Basis and dimension
  • Orthogonality and projections
  • Span and linear independence
  • Applications in feature selection and representation

4. Matrix Decompositions

  • LU decomposition
  • QR decomposition
  • Cholesky decomposition
  • Applications in solving linear systems and optimization

Practical Applications

  • Neural network weight matrices
  • Image processing and computer vision
  • Natural language processing (word embeddings)
  • Dimensionality reduction techniques
  • Optimization algorithms