Matrix representation of the "fun number triad" (that's a technical term) imaginary numbers: i^2 = -1 [0 -1] [1 0] dual numbers: e^2 = 0, e != 0 [0 1] [0 0] hyperbolic numbers: i^2 = 1, i != 1 [-1 0] [0 1]
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if you are wondering what dual numbers are useful for, i wrote up a couple things on em. here's the first: https://blog.demofox.org/2014/12/30/dual-numbers-automatic-differentiation/ … For hyperbolic numbers (also called split complex numbers, among other things), check this out: https://en.wikipedia.org/wiki/Split-complex_number#History …
