Geometric derivative

One reason I believe that log-linear dynamical systems have so much potential as a modeling tool is that they measure the relative change in quantities rather than the absolute change. For example, suppose we’re tracking the heat of a system \(h_t\). The absolute change from time \(t\) to \(t+1\) is given by \(h_{t+1} - h_t\). The relative change is given by \(h_{t+1}/h_t\). I also call the relative change the geometric change, since it is based on ratios.

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Basics: State and dynamics

I realize that most people have never learned about linear dynamical systems. It’s a pity, because it’s a very beautiful and useful area of applied math. In the next few posts I’m going to give a crash course on linear dynamical systems, which I hope will convey some sense of why they’re important. For more information check out my advisor’s class. I’ll start here with the most fundamental of the fundamentals.

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