I'm only a couple months from wrapping up a masters degree in math. The program has been great and has catered to a cohort of educators who are all seeking to drastically improve math education in our respective schools and communities. However, every time I hear the prefix eigen-, I cringe. Eigenvectors, eigenvalues, eigenspaces, you name it, for some reason these really important bits of linear algebra always gave me fits.
Math generally comes pretty easily to me, but my adviser could best be described as a linear algebraist. He really loves this stuff. Hence, it appeared in an awful lot of lectures that he gave and was largely unavoidable throughout the program, since he was instrumental in designing the curriculum that focused both on applied mathematics and math education.
Given the choice, I'll stick with calculus. As it turns out, I probably should have paid closer attention to those eigenlectures, as I bitterly called them. Today, I stumbled across an article summarizing the role that eigenvectors and linear algebra play in Google's search algorithms. Yup, that's right, my hated eigenvalues help make Google billions of dollars.
In the article's introduction, the author notes,
When Google went online in the late 1990’s, one thing that set it apart from other search engines was that its search result listings always seemed deliver the “good stuﬀ ” up front. With other search engines you often had to wade through screen after screen of links to irrelevant web pages that just happened to match the search text. Part of the magic behind Google is its PageRank algorithm, which quantitatively rates the importance of each page on the web, allowing Google to rank the pages and thereby present to the user the more important (and typically most relevant and helpful) pages ﬁrst.
I think my professor would have hugged me via email if he could have when I sent him a link not only to the article but to Maple and Mathematica demonstrations of the concepts in the article. There's a lot of math here, so it isn't for the faint of heart, but for any students struggling to see the relevance of linear algebra, or for anyone who would like an incredible primer on applied linear algebra, look no further. Cheers and happy reading!