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Topics

Vectors and Spaces

• Vector, Norm, Dot Product, Span, Subspace, Basis, Dimension, Rank

Linear Transformations

• Matrix Multiplication, Linear Map, Matrix Representation

Orthogonality and Projections

• Inner Product, Orthogonal Projection, Gram-Schmidt, Orthonormal Basis

Matrix

• Eigenvalues, Eigenvectors, Diagonalization, Jordan Form, SVD

Advanced Topics

• Pseudoinverse, Low Rank Approximation

Study Resources & Scope Used to Study

[1] Linear Algebra, 5th Edition - Friedberg, Insel, and Spence

• Vector Spaces
  • 1.2 Vector Spaces
  • 1.3 Subspaces
  • 1.5 Linear Dependence
  • 1.6 Bases and Dimension
• Linear Transformations and Matrices
  • 2.1 Linear Transformations, Null Spaces, and Ranges
  • 2.2 The Matrix Representation of a Linear Transformation
  • 2.3 Composition of Linear Transformations and Matrix Multiplication
• Diagonalization
  • 5.1 Eigenvalues and Eigenvectors
• Inner Product Spaces
  • 6.1 Inner Products and Norms
  • 6.2 The Gram-Schmidt Orthogonalization Process and Orthogonal Complements
• Canonical Forms
  • 7.1 The Jordan Canonical Form I

[2] Mathematics for Machine Learning - Deisenroth, Faisal, and Ong

• Linear Algebra
  • 2.5 Linear Independence
  • 2.6 Basis and Rank
  • 2.7 Linear Mappings
• Matrix Decompositions
  • 4.2 Eigenvalues and Eigenvectors
  • 4.5 Singular Value Decomposition
  • 4.6 Matrix Approximation

    [3] Essence of Linear Algebra - 3Blue1Brown

• Video series covering vectors, linear combinations, span, basis vectors, linear transformations, matrices, matrix multiplication, eigenvalues, and eigenvectors.

  [4] Python/NumPy Implementations

• Code for low-rank approximations.