Linear Algebra

Sub-series focused on vectors, matrices, eigen concepts, and geometric intuition for ML.

Courses

3Blue1Brown — Essence of Linear Algebra
0/16
  1. →
    Vectorsup next
  2. 2
    Linear combinations, span, and basis vectors
  3. 3
    Linear transformations and matrices
  4. 4
    Matrix multiplication as composition
  5. 5
    Three-dimensional linear transformations
  6. 6
    The determinant
  7. 7
    Inverse matrices, column space and null space
  8. 8
    Nonsquare matrices as transformations between dimensions
  9. 9
    Dot products and duality
  10. 10
    Cross products
  11. 11
    Cross products in the light of linear transformations
  12. 12
    Cramer's rule, explained geometrically
  13. 13
    Change of basis
  14. 14
    Eigenvectors and eigenvalues
  15. 15
    A quick trick for computing eigenvalues
  16. 16
    Abstract vector spaces
Gilbert Strang — MIT 18.06 Linear Algebra, Spring 2005
0/35
  1. →
    The Geometry of Linear Equationsup next
  2. 2
    Elimination with Matrices
  3. 3
    Multiplication and Inverse Matrices
  4. 4
    Factorization into A = LU
  5. 5
    Transposes, Permutations, Spaces R^n
  6. 6
    Column Space and Nullspace
  7. 7
    Solving Ax = 0: Pivot Variables, Special Solutions
  8. 8
    Solving Ax = b: Row Reduced Form R
  9. 9
    Independence, Basis, and Dimension
  10. 10
    The Four Fundamental Subspaces
  11. 11
    Matrix Spaces; Rank 1; Small World Graphs
  12. 12
    Graphs, Networks, Incidence Matrices
  13. 13
    Quiz 1 Review
  14. 14
    Orthogonal Vectors and Subspaces
  15. 15
    Projections onto Subspaces
  16. 16
    Projection Matrices and Least Squares
  17. 17
    Orthogonal Matrices and Gram-Schmidt
  18. 18
    Properties of Determinants
  19. 19
    Determinant Formulas and Cofactors
  20. 20
    Cramer's Rule, Inverse Matrix, and Volume
  21. 21
    Eigenvalues and Eigenvectors
  22. 22
    Diagonalization and Powers of A
  23. 23
    Differential Equations and exp(At)
  24. 24
    Markov Matrices; Fourier Series
  25. 25
    Quiz 2 Review
  26. 26
    Symmetric Matrices and Positive Definiteness
  27. 27
    Complex Matrices; Fast Fourier Transform
  28. 28
    Positive Definite Matrices and Minima
  29. 29
    Similar Matrices and Jordan Form
  30. 30
    Singular Value Decomposition
  31. 31
    Linear Transformations and Their Matrices
  32. 32
    Change of Basis; Image Compression
  33. 33
    Quiz 3 Review
  34. 34
    Left and Right Inverses; Pseudoinverse
  35. 35
    Final Course Review

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