L3 ENS Paris

Caroline MULLER


# I. Fundamentals:
    - linear spaces, dimension, basis
    - linear mappings
    - rank–nullity theorem
    - implications of the theorem (linear systems of equations)

# II. Matrices:
    - matrices and linear mappings
    - change of basis
    - square matrices, rank, inverse
    - determinant, eigenvalues and eigenvectors

# III. Applications:
    - waves, dispersion relations
    - linear stability analysis, chaos

Linear Algebra and Its Applications, by Peter Lax

Linear Algebra Done Right, by Sheldon Axler

Equations Differentielles Ordinaires, by V. Arnold

Nice movie of surface waves in the lab

How to cut a Parallelepiped into 6 Tetrahedrons : link