Phew, what a long ride it has been! My undergrad math research paper that I co-authored with Dr. Andrew J. Hetzel and Dr. Kent E. Morrison is finally published in MAA (Math. Assoc. of America)’s June/July 2007 Monthly.
In this article, we exhibit the results of an undergraduate research project where we asked the question: How frequently is an n x n matrix with integer entries diagonalizable over the complex numbers, the real numbers, and the rational numbers, respectively? Such a frequency is couched in terms of a variant on the number theoretic notion of “natural density.” Complete information is given for the frequency of diagonalizability over the complex numbers, and results are provided for the frequency of diagonalizability over the real numbers and the rational numbers if n = 2. At the end of the article, we provide three open questions based upon this work that may be suitable for other undergraduate research projects.
Here’s a preview (options to view in other formats are available, even in voice), courtesy of scribd:
I presented the research on this with April Jeffcoat at the AMS and MAA 2004 Joint Math Meeting in Phoenix, AZ. Here’s a picture of what appears to be perhaps one of the nerdiest time in my life. (you can drool over the sexy graphs charts behind me)
