Lecture 9: Least-Norm Solution
published: May 31, 2010, recorded: September 2007, views: 3217
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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
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