Lecture 3 | Introduction to Linear Dynamical Systems

Professor Stephen Boyd, of the Electrical Engineering department at Stanford University, gives a review of linear algebra for the course, Introduction to Linear Dynamical Systems (EE263).

Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. 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.

Complete Playlist for the Course:
http://www.youtube.com/view_play_list?p=06960BA52D0DB32B

EE 263 Course Website:
http://www.stanford.edu/class/ee263/

Stanford University:
http://www.stanford.edu/

Stanford University Channel on YouTube:
http://www.youtube.com/stanford/

Category:

Education

Tags:

• science
• electrical
• engineering
• technology
• linear
• dynamical
• system
• algebra
• control
• design
• gram
• matrix
• vector
• space
• differentiation
• research

[kiaranr]

These are truly remarkable lectures. Obviously I'm only on the 3rd one but I'm excited to go through the whole course.

It's nice to watch before bed and think about while falling asleep.

[ptkg]

Thanks Stanford for posting this. I find it disturbing there were no comments so I had to add.

[essaied66]

For the guy asking about why [-1 -1 -1 -1 -1 1 1 1 1 1 ] is not in the null space, because it has shifted the mass to the left by 5 meters let us say although at the end it has a zero velocity. The idea of the null space associated with the Force example is that we apply a set of forces but the net or the final result is the mass is back to the original position with zero velocity. I hope this helps!

[ad2181]

time 1:04 he is refering to ebonic linear algebra.

[4442627]

I can't understand that how [-1 1 -1 1 0 0 0 0 0 0] is in null space and why is

[-1-1-1-1-1 1 1 1 1 1] not in null space. Plz do reply.

[sikory]

Too bad that to see the solutions to the exercises on his site, you do need a stanford account.

[katyx72]

Practical use coming together with the theory in behind, this is really good. Thanks for Stanford.

[katyx72]

Prof. Boyd coming with a sample of practical use matching to any theory in behind which is very useful for understanding. Thanks Stanford for this fruitful course.