## Lecture 9: Least-Norm Solution

published: May 31, 2010, recorded: September 2007, views: 3217

released under terms of: Creative Commons Attribution Non-Commercial (CC-BY-NC)

# Related content

# Report a problem or upload files

If you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our**to describe your request and upload the data.**

__ticket system__*Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.*

# Description

So least norm solution. As I said last time, this is something like the dual of least squares approximate solution. So in least norm solution we’re studying the equation AX=Y. But in this case, A is fat. And we’re assuming it’s full rank, so that means you have M equations that can strain a variable X. But you have fewer equations and unknowns, so it means you have extra degrees of freedom. What that means is that AX=Y actually has lots of solutions. There are lots of solutions. It means the null space of A is more than just a zero vector. In fact, it’s exactly N minus M dimensional, the null space. So there’s a lot of freedom in choosing X. ...

See the whole transcript at Introduction to Linear Dynamical Systems - Lecture 09

# Link this page

Would you like to put a link to this lecture on your homepage?

Go ahead! Copy the HTML snippet !

## Reviews and comments:

caNNot, June 14, 2010 at 8:37 p.m.:There is a problem with the sound of this talk, it is way to slow and takes more time than the video, that is at its normal speed.

Xining Yu, September 22, 2012 at 6:53 p.m.:Just as the above comment, there is something wrong with the sound.

## Write your own review or comment: