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Linear algebra is fundamental mathematical knowledge for those who need to perform computational natural sciences. It is a neat formalism to express things in a compact way, and describe precious algorithms to solve computational problems from chemistry, physics, astronomy, and so on.

I found these precious and very clear lectures from MIT professor Gilbert Strang. The lectures are available to the general public under the MIT OpenCourseWare distant learning initiative. I am pretty sure not to say anything excessive when I claim that such initiatives should be declared Intangible Heritage of Humanity due to their important role in scientific advancement and education.

Here is the list of the lectures, linked to the proper material on the MIT OCW website:

  1. The geometry of linear equations
  2. Elimination with matrices
  3. Multiplication and inverse matrices
  4. Factorization into A=LU
  5. Transposes, permutation, spaces R^n
  6. Column space and nullspace
  7. Solving Ax=0: pivot variables, special solutions
  8. Solving Ax=b: row reduced form R
  9. Independence, basis and dimension
  10. The four fundamental subspaces
  11. Matrix spaces; rank 1; small world graphs
  12. Graphs, networks, incidence matrices
  13. Quiz 1 review
  14. Orthogonal vectors and subspaces
  15. Projections onto subspaces
  16. Projection matrices and least squares
  17. Orthogonal matrices and Gram-Schmidt
  18. Properties of determinants
  19. Determinant formulas and cofactors
  20. Cramer's rule, inverse matrix, and volume
  21. Eigenvalues and Eigenvectors
  22. Diagonalization and powers of A
  23. Differential equations and exp(At)
  24. Markov matrices; Fourier series - Quiz 2 review
  25. Symmetric matrices and positive definiteness
  26. Complex matrices; fast Fourier transform
  27. Positive definite matrices and minima
  28. Similar matrices and Jordan form
  29. Singular value decomposition
  30. Linear transformations and their matrices
  31. Change of basis; image compression
  32. Quiz 3 review
  33. Left and right inverses; pseudoinverse
  34. Final course review