Dry information: Linear code basics of machine learning

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linear algebra

• 0. Summary of key points
• 1. Vector Vector
  • 1.1 What is a vector?
  • 1.2 Vector operations
    • 1.2.1 Addition of vectors
    • 1.2.2 Multiplication of vectors
• 2. Linear Combination, Span and Basis Linear Combination, Span and Basis
  • 2.1 Operation closure
  • 2.2 Linear combination
  • 2.2 The space spanned by vectors
  • 2.3 Linear dependence and linear independence
  • 2.4 Definition of basis
• 3. Matrix and linear transformation Linear Transformation/Mapping
  • 3.1 Linear transformation
  • 3.2 Matrix and basic operations
    • 3.2.1 Matrix definition
    • 3.2.2 Matrix addition and multiplication
    • 3.2.3 Matrix multiplication
    • 3.2.4 Identity matrix
    • 3.2.5 Properties of matrices
• 5. Determinant
• 6. Inverse matrix, rank, column space, and null space
  • 6.1 Inverse matrix
  • 6.2 Rank of matrix
    • 6.2.1 Definition of rank
    • 6.2.2 Important properties of rank
  • 6.3 Column Space Column Space
  • 6.4 Null Space/Kernel
• 7. Non-square matrix
• 8. Modules, dot products and orthogonal matrices
  • 8.1 Norms of vectors
  • 8.2 Vector dot product Dot Product
  • 8.3 Positive definite matrix
  • 8.4 Angle and orthogonality
    • 8.4.1 Angle between vectors
    • 8.4.2 Orthogonal matrices
    • 8.4.3 Orthonormal basis
    • 8.4.4 Orthogonal projection (TODO)
• 9. Cross product
• 10. Basis Change
• 11. Eigenvectors, eigenvalues, eigendecomposition and singular value decomposition
  • 11.1 Eigenvectors and eigenvalues
  • 11.2 Diagonalization and eigendecomposition of matrices
  • 11.3 Singular Value Decomposition
• 12. Abstract vector space Vector Space
  • 12.1 Axioms of vector spaces
  • 12.2 Vector subspace
  • 12.3 Affine subspace