Video from the lectures is available on Canvas
Overview
Linear functions
Engineering examples
Interpretations of linear equations
Linear algebra review
Rank
Orthogonality
QR factorization
Least-squares
Example: Least-squares navigation
LS via QR factorization
Least-squares fitting
Recursive estimation
Multi-objective least-squares
Least-norm solutions of underdetermined equations
Gauss-Newton method
Eigenvectors and diagonalization
Symmetric matrices
Ellipsoids
Matrix norm
SVD and applications
Autonomous linear dynamical systems
Solution via matrix exponential
Dynamic interpretation of eigenvectors
Linear dynamical systems with inputs and outputs
Controllability and state transfer
Observability and state estimation
Summary and final comments
Example: Input design
Example: Estimation/filtering
Example: Least-squares filtering revisited
Jordan canonical form