These slides are from last year. During the quarter we will post updated versions here.

Overview

Example: Input design

Example: Estimation/filtering

Linear functions

Engineering examples

Interpretations of linear equations

Linear algebra review

Rank

Orthogonality

QR factorization

Least-squares

Example: Least-squares navigation

Example: Least-squares filtering revisited

Least-squares fitting

Recursive estimation

Multi-objective least-squares

Least-norm solutions of underdetermined equations

Eigenvectors and diagonalization

Symmetric matrices

Ellipsoids

Matrix norm

SVD and applications

Extremal-trace problems

Total least squares

Autonomous linear dynamical systems

Solution via Laplace transform and matrix exponential

Dynamic interpretation of eigenvectors

Jordan canonical form

Linear dynamical systems with inputs and outputs

Controllability and state transfer

Observability and state estimation

Summary and final comments

June 21 covered 1.1 to 6.15

June 23 covered 7.1 to 7.24