

Representing complex numbers as 2×2 matrices - TriinT
http://stochastix.wordpress.com/2008/11/09/representing-complex-numbers-as-2x2-matrices

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quilby
There seems to be an isomorphism here :-)

The function he showed _is_ an isomorphism, but those 4 properties he showed
above don't have anything to do with that (and they are also not used to prove
that that function is an iso).

EDIT: Very stupid mistake, it is not a isomorphism because it is not onto. For
example the matrix (a)ij = 1 for i=j={1,2} can not be obtained.

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TriinT
Thanks for your input. I don't know exactly what point the author wanted to
make, but IMHO his goal was to show that one can do complex arithmetic using
matrices, not to show what is and what is not an isomorphism.

I mean, other than mathematicians, no one cares what an isomorphism is, right?
But doing complex arithmetic with matrices sounds cool because one can code
stuff like Fourier transforms without a library that implements complex
numbers. I found that refreshing and interesting and that is why I submitted
this article.

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maximilian
If you implement the FFT using this matrix representation, you could have just
as easily just built your own complex number system and used that. It seems
that this matrix representation is just an easy way to not make mistakes when
doing the complex arithmetic.

Most languages make it pretty easy to implement basic complex number support.

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TriinT
Once, years ago, I created a C++ library to do complex arithmetic. All that
operator overloading made me realize that C++ is _probably_ not the most
efficient language to work with. Fortunately, Python has built-in complex
numbers...

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sethg
_sigh_ I really oughtta learn linear algebra in my Copious Free Time....

