No, you don't have to decide between the blue pill and the red pill right now, but it will be hard to escape jokes about the movie The Matrix when talking about matrices.

Sometimes, mental math isn't about being able to do math in your head quickly, but more about wrapping your head around a topic. Matrices can be especially tricky, so this post is dedicated to them.

About a year ago, TED-Ed posted a great introductory video on matrices, with a full lesson available here. I especially like the visual approach to matrix multiplication:



I do have a few criticisms of that video. First, I think they should've gone a little further, and shown a complete multiplication of a 3 by 2 and a 2 by 3 matrix, just for completeness sake. Second, did anyone else get confused by the mention of “linear algebra”? Doesn't it seem strange that a rectangular arrangement of numbers should be so important in something that begins with the word linear?

Once again, BetterExplained.com's Kalid Azar comes to the rescue with An Intuitive Guide to Linear Algebra. He takes things quite a bit slower than the video, but he does this so you can grasp all the concepts.

Kalid starts, thankfully, with an explanation of just what is so linear about matrices and linear algebra. He then shows you how to get your head around the unusual notation and multiplication. His analogy to mini-spreadsheets is a very helpful!

Probably the biggest help is the real-world example, instead of the classic vectors that are often used. He even briefly covers scary terms such as “eigenvector”.

Do take the time to go through these resources, as the matrix is a fascinating tool that shouldn't be ignored.