Course  Introduction to Linear Dynamical Systems
Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems.Topics include: Leastsquares approximations of overdetermined equations and leastnorm 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 behaviour. Multiinput multioutput systems, impulse and step matrices; convolution and transfer matrix descriptions. Control, reachability, state transfer, and leastnorm inputs. Observability and leastsquares state estimation. Prerequisites: Exposure to linear algebra and matrices. You should have seen the following topics: matrices and vectors, (introductory) linear algebra; differential equations, Laplace transform, transfer functions. Exposure to topics such as control systems, circuits, signals and systems, or dynamics is not required, but can increase your appreciation.

Lecture 1  Overview Of Linear Dynamical Systems

Lecture 2  Linear Functions (Continued)

Lecture 3  Linearization (Continued)

Lecture 4  Nullspace Of A Matrix (Continued)

Lecture 5  Orthonormal Set Of Vectors

Lecture 6  LeastSquares

Lecture 7  LeastSquares Polynomial Fitting

Lecture 8  MultiObjective LeastSquares

Lecture 9  LeastNorm Solution

Lecture 10  Examples Of Autonomous Linear Dynamical Systems

Lecture 11  Solution Via Laplace Transform And Matrix Exponential

Lecture 12  Time Transfer Property

Lecture 13  Markov Chain (Example)

Lecture 14  Jordan Canonical Form

Lecture 15  DC Or Static Gain Matrix

Lecture 16  RC Circuit (Example)

Lecture 17  Gain Of A Matrix In A Direction

Lecture 18  Sensitivity Of Linear Equations To Data Error

Lecture 19  Reachability

Lecture 20  ContinuousTime Reachability