(no subject)

[impossiblewizardry]

So in linear algebra, a big fact about linear transformations from Rⁿ to Rⁿ is that some of them are diagonalizable, and what this means is that in some ways these matrix multiplications act just like ordinary multiplications.

The eigenvalues of the rotation matrix make too much sense. You can sort of do rotation with ordinary multiplication. You can rotate in the complex plane. Turns out the eigenvalues of the matrix of rotation clockwise by θ are exp(iθ) and exp(-iθ), which rotate by θ in the complex plane.