For those who are interested, here's a lengthier explanation I wrote that relates PageRank explicitly to solving the eigenvector equation (Mq = q, in the language of the article):
Skip past the opening, and down to "Basic Description of PageRank". The article eventually gets somewhat technical, but hopefully this at least helps explain the basics. Incidentally, I don't use the term "eigenvector" in the article, but when we're analysing an equation like Mq =q, that's an eigenvector equation!
Unfortunately, in the present context, only the early part of the notes will be really accessible to someone who has only just taken an intro class in linear algebra. The later parts, which deal with issues such as how fast the PageRank algorithm converges, really require people to have more mathematical experience.
But it's not the job of such a paper to teach them about these things. This sort of paper serves as context and motivation. The material itself can, and should, be learned from other texts designed to teach it. I think what you have is an excellent piece. Read carefully at first, then skim more and more as you get lost. Inspired, go and read about some of the necessary math, then come back and get further next time.
That is exactly why I took linear algebra in college. I (tried to) read the original Google paper and was like, "eigen-what??" and decided to take the class as an elective.
Linear algebra is stupendously useful material, and I think it really should be standard in any CS curriculum. It wasn't in mine.
http://michaelnielsen.org/blog/lectures-on-the-google-techno...
Skip past the opening, and down to "Basic Description of PageRank". The article eventually gets somewhat technical, but hopefully this at least helps explain the basics. Incidentally, I don't use the term "eigenvector" in the article, but when we're analysing an equation like Mq =q, that's an eigenvector equation!