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Andrew's user avatar
Andrew
  • Member for 11 years, 6 months
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Representing quaternions as matrices
yep, It's my condition. So that isomorphism is as I told above?
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Representing quaternions as matrices
can we choose subfield closed so q^2=-a and p^2=-b hence we have representation i=((q,0),(0,-q)) and j=((0,p),(-p,0))?
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Representing quaternions as matrices
ok, how to represent generalised quaternions A(a,b) using 2*2 matrices? I need this, cuz I want to prove isomorphism between generalised quaternions over F and matrix 2*2 over F. Thanks!
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Representing quaternions as matrices
But Artin–Wedderburn theorem claim that there is 2*2 matrix over F exists.
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Representing quaternions as matrices