It seems appropriate to start with a declaration of intent. First, for full disclosure: I wanted the blog to be called "The Null Space," but that name (with and without "the") was taken. Now that that piece of fascinating trivia is behind us: a nullspace of a matrix A is the subspace composed of all vectors x such that Ax=0.

What? You don't get it? While nullspaces are packed with fascinating characteristics, here's the deal: they contain all the solutions to certain types of differential and difference equations, including sexy beasts like Markov processes. Oh, yeah!

Still don't get it? Nullspaces hold the solutions to (some broad types of) dynamic problems. These little beasts (the set of eigenvectors, together with their inseparable lovers, the eigenvalues) provide information about the path, stability, and final resting place, if any, of systems represented in those dynamic problems.

And what is a blog about if not about trying to make sense of that dynamic mess out there, aim for a little more stability in your path, find your own steady state?

Hmmm. OK, that was horrible. The truth is, I really liked "the nullspace" since I heard the word in math camp of the Econ PhD program and decided I had to open a bar named that one day. I haven't opened a bar; I opened a blog.

...

p.s. since you were just dying to know, "kernel" means the same in linear algebra... but not in all branches of mathematics. See how nuanced and insightful this blog is from the get go?

## 1 comment:

OMG... you should be back in school as a professor, where you can continue to do research and hold on to that Ph.D. ; )

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