Professor Stephen Boyd, of the Electrical Engineering department at Stanford University, lectures on the least norm solutions of undetermined equations for the course, Introduction to Linear Dynamical Systems (EE263).

1. Introduction
2. Linear Functions
3. LInear Algebra Review
4. Orthonormal Sets of Vectors and QR Factorization
5. QR Factorization and Least Squares
6. Applications of Least Squares
7. Regularized Least Squares and the Gauss-Newton Method
8. Least Norm Solutions of Undetermined Equations
9. Autonomous Linear Dynamical Systems
10. Autonomous Linear Dynamical Systems
11. Matrix Exponentials
12. Matrix Exponentials, Eigenvectors and Diagonalization
13. Jordan Canonical Form
14. Applications of Jordan Canonical Form
15. Symmetric Matrices
16. Symmetric Matrices, Quadratic Forms and Matrix Norm
17. Applications of Single Value Decomposition in LDS
18. Applications of SVD, Controllability, and State Transfer in Electrical Engineering
19. Controllability, and State Transfer in Electrical Engineering (cont.)
20. Observability and State Estimation

In this course, Professor Stephen P. Boyd gives 20 video lectures on the concepts of Linear Dynamical Systems. He gives an introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares approximations 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. EE263 covers some of the same topics, but is complementary to, CME200.

Tags: Math, Math L.D.S.