Bill Shillito has made some pretty cool and very informative math videos on YouTube. Check them out here.
Still have questions after watching this video? Check out Bill's follow up video here.
There are numerous applications of matrices, both in mathematics and other sciences. Some of them merely take advantage of the compact representation of a set of numbers in a matrix. For example, in game theory and economics, the payoff matrix encodes the payoff for two players, depending on which out of a given (finite) set of alternatives the players choose. Text mining and automated thesaurus compilation makes use of document-term matrices such as tf-idf to track frequencies of certain words in several documents.
Keanu Reeves' virtual world in the The Matrix (I guess we can call all three movies "The Matrices") have more in common with this tutorial than you might suspect. Matrices are ways of organizing numbers. They are used extensively in computer graphics, simulations and information processing in general. The super-intelligent artificial intelligences that created The Matrix for Keanu must have used many matrices in the process. This tutorial introduces you to what a matrix is and how we define some basic operations on them.
The Matrix is a movie made in 1999. It's about "a computer hacker learns from mysterious rebels about the true nature of his reality and his role in the war against its controllers."
Somebody asked the Yahoo community why it's impossible to divide matrices. See the conversation here. In the same way, this blogger (obviously someone who uses matrices for his job on a daily basis) argues that you can in fact divide matrices. What is going on here? Can you or can't you divide matrices? Share your answer in the appropriate place in the open answer questions in the think section.
In a lively show, mathemagician Arthur Benjamin races a team of calculators to figure out 3-digit squares, solves another massive mental equation and guesses a few birthdays. How does he do it? He’ll tell you.

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