Archive for March 2011

Graphs, maps, and geocoding

Jim Hufford, Esq. had his first Stata lesson: “This is going to be awesome when I understand what all those little letters and things mean.”

Along those lines—awesome—Jim may want to see these nice Stata scatterplots from the “wannabe economists of the Graduate Institute of International and Development Studies in Geneva” at Rigotnomics.

If you want to graph data onto maps using Stata—and see another awesome graph—see Mitch Abdon’s “Fun with maps in Stata” over at the Stata Daily.

And if you’re interested in geocoding to obtain latitudes and longitudes from human-readable addresses or locations, see Adam Ozimek’s “Computers are taking our jobs: Stata nerds only edition” over at Modeled Behavior and see the related Stata Journal article “Stata utilities for geocoding and generating travel time and travel distance information” by Adam Ozimek and Daniel Miles.

Pi is (still) wrong

See this video, by Vi Hart:

This link was passed on to me by my friend Marcello. I’ve been bold enough to make up words such as eigenaxis and eigenpoint, but it takes real courage to suggest redefining π, even when you’re right!

After seeing the video, you can go here and here to learn more about what is being proposed.

Don’t click on comments until you’ve seen the video. Ms. Hart does a better job presenting the proposal than any of us can.

Categories: Mathematics Tags: ,

Understanding matrices intuitively, part 2, eigenvalues and eigenvectors

Last time, I showed you a way to graph and to think about matrices. This time, I want to apply the technique to eigenvalues and eigenvectors. The point is to give you a picture that will guide your intuition, just as it was previously.

Before I go on, several people asked after reading part 1 for the code I used to generate the graphs. Here it is, both for part 1 and part 2: Read more…

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Categories: Blogs Tags:

Understanding matrices intuitively, part 1

I want to show you a way of picturing and thinking about matrices. The topic for today is the square matrix, which we will call A. I’m going to show you a way of graphing square matrices, although we will have to limit ourselves to the 2 x 2 case. That will be, as they say, without loss of generality. The technique I’m about to show you could be used with 3 x 3 matrices if you had a better 3-dimensional monitor, and as will be revealed, it could be used on 3 x 2 and 2 x 3 matrices, too. If you had more imagination, we could use the technique on 4 x 4, 5 x 5, and even higher-dimensional matrices. Read more…