Matrix—The Meeting
That’s how it is with people. Nobody cares how it works as long as it works—Councillor Hamann
Santosh Vempala and Nikhil Srivastava announced the first in hopefully a series of online meetings about matrix algorithms. Not about the Matrix—the—movie. Santosh and Nikhil said: we expect to have an attendance of 
Today I thought we would talk about the Zoom meeting and future ones being planned.
Zoom feels closer to the world of the Matrix movies. If you haven’t seen them, all you need to know is the premise of humanity being diverted in a virtual reality. How do we know the little figures in those boxes are real people? More concretely, it seems obvious to Ken and me that simulated human online agents will arrive much earlier than person-like robots.
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Matrix Reloaded virtual background |
In particular, how much does it take to automate giving a lecture online? Ken has spent much time this term upgrading his lecture notes in two courses to broadcast quality. Delivering them remotely trades against the spontaneity of drawing pictures on a whiteboard or document camera and developing proofs and algorithms step-by-step. It should be easier to develop an AI capable of reacting to questions put in Zoom chat than with in-class situations, where “reading the room” is also important for modulating the speed and manner of presentation.
The Meetings
Daniel Kressner, Mike Mahoney, Cleve Moler, Alex Townsend, and Joel Tropp were also organizers of this smeeting on matrix computation. This Wednesday was the first in a series of online meetings. The speakers for today were Peter Bürgisser, Nick Higham, and Cameron Musco, and the panelists were Jim Demmel, Ilse Ipsen, and Richard Peng.
The blurb for the meetings is:
We are organizing an online seminar series on “Complexity of Matrix Computations”, whose goal is to bridge the gap between how numerical linear algebra and theoretical computer science researchers view and study the fundamental computational problems of linear algebra. This gap includes foundational issues such as: what is the computational model? What does it mean to solve a problem? On which criteria do we compare algorithms? We also hope to discuss which techniques in theoretical computer science might be useful in numerical linear algebra and vice versa.
I love seeing the words “fundamental” and “foundational”, and one question resonated even more.
The Question
What does it mean to solve a problem? In this case what does it mean to solve a linear equation? This is the question that was discussed the most—especially at the end of the meeting.
I have always thought there is an answer to this. The answer is based on asking what the client wants. Imagine Alice is asked by Bob to solve a linear system
Alice could go off and return the 
I believe the right answer is: Alice should ask Bob:
Bob, what will you do with the answer to this?
Bob could say, for example:
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I plan to compute the inner product of
for some
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I plan to see what the norm of
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Or, I plan to see what
is.
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Or, I could be just happy to know that there is some
- Or, and so on.
Thus, I believe, the answer only makes sense if Alice knows what will be done next with the “solution”. What do you think?
One View
What does it mean to solve the equation 
Jim Demmel’s view is captured in his notes that he was kind enough to download to the site SLACK.
Open Problems
What do you think about this series of meetings? Did you attend them initially? Will you look in next time so we can break 200 attendees?
Santosh says: To join the seminar, please send an email
Join Zoom
after adding the subject “join”. Information about how to connect to the Zoom conference call will be circulated via email to all registered attendees prior to each seminar.
It is reasonable question to ask what you plan to do with the result (even in the one dimensional problem). If you use floating point arithmetic there is always a degree of approximation to the answer, and the algorithm you choose would depend on what you want to do.
Imagine solving A x = 1, (A is a floating point number very close to 1). How I do this may depend on whether the subsequent computation needs x-1 or x+1.