Stats Made Easy

Practical Tools for Effective Experimentation

Sunday, April 27, 2008

Musings on matrices

Evidently due to its concentration algorithmic ‘philic’ minds, Stat-Ease gets review copies of new technical tomes from the Society for Industrial and Applied Mathematics (SIAM). I once fancied myself as a ‘mathelete,’ but I learned differently after moving up from being the big fish in my small pond at high school to a miniscule minnow at a major university in the Midwestern USA. My mistake was skipping into an advanced calculus class populated by some of the country’s top talent – National Merit scholars like me. Very quickly I realized that my math skills only put me on the very bottom rung and that only by the very tip of one fingernail. What saved me was begging for mercy by the teacher who, luckily, was sick and tired of the smart-mouths in the class who really got it and made sure to flout their chops in math. Thus, when the newest SIAM publication arrives, I always look it over in wonder before quickly passing it along to our master’s statisticians and algorithmic programmers, who may understand its true value.

For example, the book this week is Functions of Matrices, Theory and Computation by Nicholas J. Higham, which “emphasizes Schur decomposition, block Parlett recurrence, and judicious use of Padé approximants.” That blew me away immediately, but I rifled through the pages anyways and found a few pages of interest on the history of matrix functions, which really are useful in our business of experiment design and statistical analysis. (Thank goodness for the power of computers to do the calculations!) Higham credits English-born James Joseph Sylvester as the inventor of the matrix (not to be confused with the famous movie trilogy!). Sylvester emigrated to the USA where he founded the American Journal of Mathematics in 1878, the self-proclaimed “oldest mathematics journal in the Western Hemisphere in continuous publication.”

What amazes me is that anyone can read such esoteric materials, but it’s good they do, because great advances are made possible by developments in math. For example, Higham points out that the first practical application of matrices led to the elimination of unwanted flutter in aircraft wings. (Galloping flutter, or wake vortex flutter, caused the spectacular failure of the Tacoma Narrows Bridge in 1940.*) This work was done by the Aerodynamics Department of England’s National Physical Laboratory (NPL) in the 1930s. In parallel, not far away in the UK, Ronald Fisher, the founder of modern-day applied statistics, was developing the core catalog of experimental design matrices that still remain in use today.

“Here I stand because of you, Mr. Anderson. Because of you, I'm no longer an Agent of this system. Because of you, I've changed. I'm unplugged.”
– Agent Smith (played by Hugo Weaving ) from The Matrix Reloaded (2003)

PS. Neither the quote nor the picture really have much to do with matrices, but they provide me some amusement. For example, I saw the second movie of the Matrix trilogy with my brother Paul, an techie type like me. We annoyed the exiting theater patrons greatly by regurgitating Agent Smith’s lines about “Mr. Anderson” this and “Mr. Anderson” that – all with gagging glee.

The picture exhibits a physical matrix – the screen window. I just inserted all the screens earlier this week when it seemed as if Spring had finally arrived in Minnesota. However, we citizens of this northern State were chagrined to see a coating of snow yesterday morning – over a foot in some parts. :(

*If you’d like to set up an experiment on flutter that requires only a hair blower and some other materials that can be procured from your local hardware store, see this posting on Aeroelasticity Phenomenon by Wright State's College of Engineering and Computer Science (Dayton, Ohio).


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