Concepts familiar from grade-school algebra have broad ramifications in computer science.
Larry Hardesty, MIT News Office
Among the most common tools in electrical engineering and computer science are rectangular grids of numbers known as matrices. The numbers in a matrix can represent data, and they can also represent mathematical equations. In many time-sensitive engineering applications, multiplying matrices can give quick but good approximations of much more complicated calculations.
Matrices arose originally as a way to describe systems of linear equations, a type of problem familiar to anyone who took grade-school algebra. “Linear” just means that the variables in the equations don’t have any exponents, so their graphs will always be straight lines.
The equation x – 2y = 0, for instance, has an infinite number of solutions for both x and y, which can be depicted as a straight line that passes through the points (0,0), (2,1), (4,2), and so on. But if you combine it with the equation x – y = 1, then there’s only one solution: x = 2 and y = 1. The point (2,1) is also where the graphs of the two equations intersect.
The matrix that depicts those two equations would be a two-by-two grid of numbers: The top row would be [1 -2], and the bottom row would be [1 -1], to correspond to the coefficients of the variables in the two equations. Read more.
Want to learn more about matrices? Professor Gilbert Strang can help.