• 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.