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What is eigenvalue decomposition and why would it be useful in games?

In various math libraries developed for game engines, I see 2x2 and 3x3 square matrices having this function (along with some helper functions). I tried to find information regarding it but did not come across game specific material (wikipedia entry is quite heavy and does not relate to games).

It would be great if in your answer, you could provide an example or two on how it is used in games.