Linear algebra is the study vectors and vector spaces, while matrices are essentially grids of numbers used to solve some problems in linear algebra. If that sounds hard and complicated, that’s because it can be. Many colleges dedicate entire courses to the study of this one topic. However, the basics of matrices and linear algebra aren’t too bad, and can even be fun.
Here is a list of just some of the professions that need to have a knowledge of this math topic:
- Aeronautical Engineers – This profession designs aircraft, and matrices are incredibly important to that (assuming you want your plane to stay in the air). Some of these matrices can get fairly large (12×12, for example), and while they would be very difficult to solve by hand, they are fairly easy to solve using computers (Phillips, 2010).
- Computer Programmers – Speaking of solving things using computers, programmers heavily rely on matrices (though they often call them arrays). Many programming languages use them, and not just for science; most graphics are essentially matrices containing color information for each pixel.
- Ecologists – It may be hard to believe, but ecosystems are complicated things. To prove changes over time and distance weren’t due to random chance, ecologists often use a statistical test called PERMANOVA to test their hypotheses (“Permutational analysis of variance”, n.d.). This test relies on matrices to properly set it up.
- Civil Engineering – In the same way that people don’t want their planes to suddenly stop moving, most people prefer their bridges to not suddenly start. To accomplish this, each individual beam that is part of the bridge has to be evaluated for how much weight it carries, and this is most effectively done using linear algebra.
- Robotics – When working in robotics, it is often easier to think about multiple pieces of the machine having their own coordinate systems (Hiob, 1998). To go back and forth between them, you can use matrices.
This is just a small sampling of the different uses of matrices and linear algebra. While they may be tricky at first glance, they are powerful tools in many fields.
Now are you glad that you took the red pill and learned just a bit more about the uses of a matrix?
Hiob, E. (1998, June 11). Robotics: Using transformation matrices to change from one coordinate system to another in robotics. Retrieved July 16, 2017, from http://commons.bcit.ca/math/examples/robotics/linear_algebra/index.html
Permutational analysis of variance. (n.d.) In Wikipedia. Retrieved July 16, 2017, from https://en.wikipedia.org/wiki/Permutational_analysis_of_variance
Phillips, W. F. (2010). Mechanics of flight (2nd ed). Hoboken, N.J: J. Wiley.