HAS202X - Linear algebra for sciences and engineering

Documents

Link to all ressources on Moodle.

Contents

1) Matrices and vector spaces

• Matrix operations, powers, properties and computations
• Special types of matrices
• Matrix vector space, subspaces
• $\mathbb{R}^n$ seen as the space of column matrices

2) Linear systems and determinants

• Solving linear systems using Gaussian elimination
• Solution space of a system
• Determinants in dimension 2 and 3
• Invertible matrices and applications to linear systems

3) Bases, coordinates, and change of basis

• Bases in $\mathbb{R}^n$, coordinates
• Intuitive notion of dimension
• Change of basis and transition matrices

4) Linear maps and diagonalization

• Linear maps from $\mathbb{R}^p$ to $\mathbb{R}^n$
• Matrix representation with respect to a basis
• Change of basis formula
• Basic diagonalization (only 2×2 and 3×3 examples)
• Application to linear differential systems
• Matrix exponential and introduction to nonlinear systems

Main responsible: Laurent Guieu