Explained: Matrices (MIT News)

Concepts familiar from grade-school algebra have broad ramifications in computer science.

Larry Hardesty, MIT News Office

A matrix multiplication diagram. (Image: MIT News.  All rights reserved.)

A matrix multiplication diagram. (Image: MIT News. All rights reserved.)

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.

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