Videos at MATH 152: Koofers

1:09:02

Overview Of Linear Dynamical Systems, Why Study Linear Dynamical Systems?, Examples Of Linear Dynamical Systems, Estimation/Filtering Example, Linear Functions And Examples

Author: Stephen Boyd Views: 1

1:11:42

Linear Functions (Continued)

Linear Functions (Continued), Interpretations Of Y=Ax, Linear Elastic Structure, Example, Total Force/Torque On Rigid Body Example, Linear Static Circuit Example, Illumination With Multiple Lamps Exam..

Author: Stephen Boyd Views: 1

1:08:55

Linearization (Continued)

Linearization (Continued), Navigation By Range Measurement, Broad Categories Of Applications, Matrix Multiplication As Mixture Of Columns, Block Diagram Representation, Linear Algebra Review, Basis An..

Author: Stephen Boyd Views: 1

1:13:37

Nullspace Of A Matrix (Continued)

Nullspace Of A Matrix(Continued), Range Of A Matrix, Inverse, Rank Of A Matrix, Conservation Of Dimension, 'Coding' Interpretation Of Rank, Application: Fast Matrix-Vector Multiplication, Change Of Co..

Author: Stephen Boyd Views: 0

1:15:14

Orthonormal Set Of Vectors

Orthonormal Set Of Vectors, Geometric Interpretation, Gram-Schmidt Procedure, General Gram-Schmidt Procedure, Applications Of Gram-Schmidt Procedure, 'Full' QR Factorization, Orthogonal Decomposition ..

Author: Stephen Boyd Views: 0

1:16:19

Least-Squares

Least-Squares, Geometric Interpretation, Least-Squares (Approximate) Solution, Projection On R(A), Least-Squares Via QR Factorization, Least-Squares Estimation, Blue Property, Navigation From Range Me..

Author: Stephen Boyd Views: 0

1:15:46

Least-Squares Polynomial Fitting

Least-Squares Polynomial Fitting, Norm Of Optimal Residual Versus P, Least-Squares System Identification, Model Order Selection, Cross-Validation, Recursive Least-Squares, Multi-Objective Least-Square..

Author: Stephen Boyd Views: 0

1:15:58

Multi-Objective Least-Squares

Multi-Objective Least-Squares, Weighted-Sum Objective, Minimizing Weighted-Sum Objective, Regularized Least-Squares, Laplacian Regularization, Nonlinear Least-Squares (NLLS), Gauss-Newton Method, Gaus..

Author: Stephen Boyd Views: 0

1:09:02

Least-Norm Solution

Least-Norm Solution, Least-Norm Solution Via QR Factorization, Derivation Via Langrange Multipliers, Example: Transferring Mass Unit Distance, Relation To Regularized Least-Squares, General Norm Minim..

Author: Stephen Boyd Views: 0

1:11:42

Examples Of Autonomous Linear Dynamical Systems

Examples Of Autonomous Linear Dynamical Systems, Finite-State Discrete-Time Markov Chain, Numerical Integration Of Continuous System, High Order Linear Dynamical Systems, Mechanical Systems, Lineariza..

Author: Stephen Boyd Views: 1

1:08:55

Solution VIa Laplace Transform And Matrix Exponential

Solution Via Laplace Transform And Matrix Exponential, Laplace Transform Solution Of X_^ = Ax, Harmonic Oscillator Example, Double Integrator Example, Characteristic Polynomial, Eigenvalues Of A And P..

Author: Stephen Boyd Views: 1

1:13:37

Time Transfer Property

Time Transfer Property, Piecewise Constant System, Qualitative Behavior Of X(T), Stability, Eigenvectors And Diagonalization, Scaling Interpretation, Dynamic Interpretation, Invariant Sets, Summary, M..

Author: Stephen Boyd Views: 0

1:13:01

Markov Chain (Example)

Markov Chain (Example), Diagonalization, Distinct Eigenvalues, Digaonalization And Left Eigenvectors, Modal Form, Diagonalization Examples, Stability Of Discrete-Time Systems, Jordan Canonical Form, G..

Author: Stephen Boyd Views: 2

1:17:42

Jordan Canonical Form

Jordan Canonical Form, Generalized Modes, Cayley-Hamilton Theorem, Proof Of C-H Theorem, Linear Dynamical Systems With Inputs & Outputs, Block Diagram, Transfer Matrix, Impulse Matrix, Step Matrix

Author: Stephen Boyd Views: 0

1:09:01

DC Or Static Gain Matrix

DC Or Static Gain Matrix, Discretization With Piecewise Constant Inputs, Causality, Idea Of State, Change Of Coordinates, Z-Transform, Symmetric Matrices, Quadratic Forms, Matrix Nom, And SVD, Eigenva..

Author: Stephen Boyd Views: 0

1:12:35

RC Circuit (Example)

RC Circuit (Example), Quadratic Forms, Examples Of Quadratic Form, Inequalities For Quadratic Forms, Positive Semidefinite And Positive Definite Matrices, Matrix Inequalities, Ellipsoids, Gain Of A Ma..

Author: Stephen Boyd Views: 0

1:16:52

Gain Of A Matrix In A Direction

Gain Of A Matrix In A Direction, Singular Value Decomposition, Interpretations, Singular Value Decomposition (SVD) Applications, General Pseudo-Inverse, Pseudo-Inverse Via Regularization, Full SVD, Im..

Author: Stephen Boyd Views: 0

1:15:14

Sensitivity Of Linear Equations To Data Error

Sensitivity Of Linear Equations To Data Error, Low Rank Approximations, Distance To Singularity, Application: Model Simplification, Controllability And State Transfer, State Transfer, Reachability, Re..

Author: Stephen Boyd Views: 0

1:10:30

Reachability

Reachability, Controllable System, Lest-Norm Input For Reachability, Minimum Energy Over Infinite Horizon, Continuous-Time Reachability, Impulsive Inputs, Least-Norm Input For Reachability

Author: Stephen Boyd Views: 0

1:09:25

Continuous-Time Reachability

Continuous-Time Reachability, General State Transfer, Observability And State Estimation, State Estimation Set Up, State Estimation Problem, Observability Matrix, Least-Squares Observers, Some Parting..

Author: Stephen Boyd Views: 0