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:

- The geometry of linear equations
- Elimination with matrices
- Multiplication and inverse matrices
- Factorization into A=LU
- Transposes, permutation, spaces R^n
- Column space and nullspace
- Solving Ax=0: pivot variables, special solutions
- Solving Ax=b: row reduced form R
- Independence, basis and dimension
- The four fundamental subspaces
- Matrix spaces; rank 1; small world graphs
- Graphs, networks, incidence matrices
- Quiz 1 review
- Orthogonal vectors and subspaces
- Projections onto subspaces
- Projection matrices and least squares
- Orthogonal matrices and Gram-Schmidt
- Properties of determinants
- Determinant formulas and cofactors
- Cramer’s rule, inverse matrix, and volume
- Eigenvalues and Eigenvectors
- Diagonalization and powers of A
- Differential equations and exp(At)
- Markov matrices; Fourier series – Quiz 2 review
- Symmetric matrices and positive definiteness
- Complex matrices; fast Fourier transform
- Positive definite matrices and minima
- Similar matrices and Jordan form
- Singular value decomposition
- Linear transformations and their matrices
- Change of basis; image compression
- Quiz 3 review
- Left and right inverses; pseudoinverse
- Final course review