In February of 2011, I gave a talk to the Dartmouth Math Club about linear algebra. This post replicates the page of resources I made for the club members related to that talk, and adds one new one.
- Slides from the talk.
- Pdf about uses of linear algebra. From Oliver Knill, Harvard Math, near the bottom of this page, which has a large number of other handouts about linear algebra in general and applications.
Vector graphics
- Some Adobe Photoshop help. Unfortunately you have to go to the index and click V to find the vector graphics segment, but it is the source of the bicycle graphic in my slides and has a nice explanation.
- Interactive Mathematics’ vector art page, with explanation of more of the math behind the pictures and links to lots of other pages.
- Inkscape is a free drawing program that makes vector graphics natively. They have many useful tutorials and you can find even more elsewhere on the web.
Google PageRank
Markov chains
- Fun With Markov Chains. Has examples where Alice in Wonderland was mixed together with either Hamlet or the Biblical books of Genesis and Revelation.
- Generating Text, Jon Bentley. Has examples where the King James Bible was remixed, and where his own text Programming Pearls was remixed.
Note: the friend I corralled into compiling the C code for me said the first link’s program gave immense amounts of output without seeming to be near an end, whereas the second program gave much more reasonable files. I suspect based on the files I received that the amount of output in the second case is proportional to the amount of input. Reading the first page indicates you can specify the number of words of output in the command line; I don’t know if my friend did that. - Random Word Generator
- Mark V. Shaney text generator
More details on the example in the slides above:
The Robert Frost poems included were Birches, Come In, Desert Places, Mending Wall, Nothing Gold Can Stay, On Looking Up by Chance at the Constellations, Reluctance, and Stars. The Dr. Seuss books included were One Fish, Two Fish, Red Fish, Blue Fish, and The Sneetches. The full recombined text may be found here, though I only put line breaks into the first third or so. The rest is unmined for Seufrostian gems. I tried putting a combination of the Dartmouth Marching Band song lyrics (only the songs related to Dartmouth, of course), and the standard description of Daniel Webster’s closing in the Dartmouth Case, but it did not turn up much of anything. If you don’t want to compile the C code in one of the first two links, Mark V. Shaney could be the answer. If it turns up any pearls let me know!
Principal component analysis
- Source of graphic in the slides.
- Chapter on PCA. Long, but a good example and overview at the start. This links directly to the pdf; I was unable to find a descriptive page for it.
Miscellaneous Fun
We’ll close with the only linear algebra joke I found worth sharing, a limerick by Donald E. Simanek.
Null vectors have zero projection.
So you ask, “What can be their direction?”
They point any which way.
“That’s magic!” you say?
Not really; it’s just misdirection.