Advanced Linear Algebra - Lecture 40: The Operator Norm of a Matrix

We introduce the operator norm of a matrix, and demonstrate how to compute it via the singular value decomposition. We also present some related results about the Frobenius norm.

Please leave a comment below if you have any questions, comments, or corrections.

Timestamps:
00:00 - Introduction
01:22 - Definition
04:35 - Submultiplicativity and unitary invariance
13:51 - Computation via singular values
20:49 - 3x3 example

[swat_katz_tbone]

Wonderful lecture !!!! I have no doubt that your lecture series on Advanced Linear Algebra is going to become a gold standard in the future.

[quantabot]

I have been listening to this series for nearly 2 months now, Time listening to this series is time well spent on learning linear algebra

[kaustuvray]

Wish I had found this channel earlier. Lectures are short and to the point.
loved it.
Thank you !

[alileo]

It was a perfect lecture video for my Numerical Analysis course which made me understand everything about those norms and had me able to write down proofs so easily. Thanks for that <3

[sarahli]

Dear Dr. Johnston, thank you so much for the great lectures! The explanation is so clear, and the intuition is well-illustrated. Thanks for your time and efforts to make such great teaching materials!!! Really appreciate it.

[caseyj]

You have made so many concepts I was confused about click! Thank you 😊

[ggggggggsdgdag]

Thank you for explaining concepts intuitively. I don't know why my professor cannot do that.

[hibaal-taher]

such a beautiful and smooth explanation !! Thank you sir

[caseyj]

here i am rewatching a year later. thank you!

[karansehgal]

What is the difference between a spectral norm and an operator norm in terms of using the singular values of a matrix for their calculation? Could you please explain this using the example you gave at the end of the video?

[barrelroller]

Brilliant lecture, thanks a lot! I only a bit confused that the largest vector which represents the matrix transformation was not called eigenvector (so it's length would be the eigenvalue). Are they actually applicable terms in this context?