• Kogasa@programming.dev
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    5 months ago

    Yup, you’ll notice the only thing distinguishing C from R^(2) is that multiplication. That one definition has extremely broad implications.

    For fun, another definition is in terms of 2x2 matrices with real entries. The identity matrix

    1 0
    0 1
    

    is identified with the real number 1, and the matrix

    0 1
    -1 0
    

    is identified with i. Given this setup, the normal definitions of matrix addition and multiplication define the complex numbers.