These slides are updated as the course progresses, so we don't recommend downloading them all at the beginning of the quarter.

Overview

Linear functions

Engineering examples

Interpretations of linear equations

Linear algebra review

Range and null space

Rank

Orthogonality

QR factorization

Least-squares

Example: Least-squares navigation

Multi-objective least-squares

Least-norm solutions of underdetermined equations

Gauss-Newton method

Least-squares fitting

LS via QR factorization

Recursive estimation

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