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I'm looking for a computer program that can do symbolical (i.e. not numerical) algebraic calculations. It doesn't have to do anything absurdly complicated, but it has to be able to multiply complex matrices. For example if I know that an arbitrary SU(2) matrix [itex]\lambda[/itex] can be expressed as
[tex]\lambda=\begin{pmatrix}a& b\\ -b^*& a^*\end{pmatrix}[/tex]
then what is
[tex]\sum_{i=1}^3 x^i \lambda\sigma_i\lambda^\dagger[/tex]
where the [itex]\sigma_i[/itex] are the Pauli spin matrices? I came across this expression the other day, and I decided that I don't care enough about the result to do the calculation explicitly.
I also thought that there must be some kind of software that makes this sort of thing easy.
So...can someone recommend a program that can do this sort of thing?
[tex]\lambda=\begin{pmatrix}a& b\\ -b^*& a^*\end{pmatrix}[/tex]
then what is
[tex]\sum_{i=1}^3 x^i \lambda\sigma_i\lambda^\dagger[/tex]
where the [itex]\sigma_i[/itex] are the Pauli spin matrices? I came across this expression the other day, and I decided that I don't care enough about the result to do the calculation explicitly.
I also thought that there must be some kind of software that makes this sort of thing easy.So...can someone recommend a program that can do this sort of thing?