LINEAR ALGEBRA

L3 ENS Paris

L3 ENS Paris

Caroline MULLER

- Linear Algebra - Syllabus

# 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 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

- Books

Linear Algebra and Its Applications, by Peter Lax

Linear Algebra Done Right, by Sheldon Axler

Equations Differentielles Ordinaires, by V. Arnold

Linear Algebra Done Right, by Sheldon Axler

Equations Differentielles Ordinaires, by V. Arnold

- Links