Lectures (Video)
- 1. Overview
- 2. Linear Functions
- 3. Linear algebra review
- 4. Orthonormal sets of vectors and QR factorization
- 5. Least-squares
- 6. Least-squares applications
- 7. Regularized least-squares and Gauss-Newton method
- 8. Least-norm solutions of underdetermined equations
- 9. Autonomous linear dynamical systems
- 10. High Order Linear Dynamical Systems
- 11. Solution via Laplace transform and matrix exponential
- 12. Eigenvectors and diagonalization
- 13. Jordan canonical form
- 14. Linear dynamical systems with inputs and outputs
- 15. Eigenvalues Of Symmetric Matrices
- 16. Symmetric matrices, quadratic forms, matrix norm, and SVD
- 17. SVD applications
- 18. Example: Quantum mechanics
- 19. Controllability and state transfer
- 20. Observability and state estimation
Introduction to Linear Dynamical Systems
Course Summary
This course is based on Introduction to Linear Dynamical Systems EE263 made available by Stanford University: Stanford Engineering Everywhere under the Creative Commons Attribution 3.0 license.
This course is an introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. (Includes a full set of video lectures.)
Topics include: Least-squares aproximations of over-determined equations and least-norm solutions of underdetermined equations. Symmetric matrices, matrix norm and singular value decomposition. Eigenvalues, left and right eigenvectors, and dynamical interpretation. Matrix exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution and transfer matrix descriptions. Control, reachability, state transfer, and least-norm inputs. Observability and least-squares state estimation.
Reading Material
1. Textbook (MIT 18.06): Introduction to Linear Algebra. 3rd ed.Strang, Gilbert. Introduction to Linear Algebra. 3rd ed. Wellesley, MA: Wellesley-Cambridge Press, March 2003. ISBN: 0961408898.
(Click the button below to see a preview of the book)
Course Material
1. Matrix primer notes(a) Matrix primer (lecture 1 slides)
(b) Matrix primer (lecture 2 slides)
(c) Matrix primer (lecture 3 slides)
2. Crimes against matrices
3. Basic notation
4. Least squares and least norm solutions using Matlab
5. Solving general linear equations using Matlab
6. Low rank approximation and extremal gain problems
