Arthur Cayley and James Joseph Sylvester, who invented matrices in the 1850s, are said to have thought they had produced a nice bit of maths, but it would be of no practical use.

*Arthur Cayley: pioneer in group theory, invariant theory, and matrix theory*

Cayley and Sylvester were spectacularly wrong about that. Matrix algebra is probably more widely used than any other bit of maths beyond the basic calculation methods learned at GCSE.

“Matrix” is the only mathematical concept whose use has spread widely enough to give its name to a series of Hollywood blockbuster films.

Here is a short summary of just some uses of matrices. There are many beyond those: for example, in economics, and in IT, such as the gigantic matrices used for the Google search algorithm.

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