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Thread: Isomorphich question

  1. #1
    ux0
    ux0 is offline
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    Isomorphich question

    this is a two part question...

    1) i need to prove that the set F of all the 2x2 real matrices of the form

    $\displaystyle A = \begin{bmatrix}
    a & b\\
    -b & a
    \end{bmatrix}$

    is a field with operations matrix addition and matrix multiplication.


    2) Prove that F is isomorphic to $\displaystyle \mathbb{C}$

    I was gonna define

    $\displaystyle \varphi : F \to \mathbb{C}$ by $\displaystyle \varphi (A)=a+ib$...

    i think this is obvious but not sure where to go here.. because if we are talking about real matrices, then how can it be isomorphic to a complex numbers?
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  2. #2
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    The link Representing complex numbers as 2×2 matrices Rod Carvalho's web notebook might help with part two, but for part one I'm not sure . . .
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