Can someone recommend a good computer program?

[Fredrik]

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 $\lambda$ can be expressed as

$$\lambda=\begin{pmatrix}a& b\\ -b^*& a^*\end{pmatrix}$$

then what is

$$\sum_{i=1}^3 x^i \lambda\sigma_i\lambda^\dagger$$

where the $\sigma_i$ 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?

 

[neutrino]

For free software, try http://maxima.sourceforge.net/

 

[tacman]

There are several computer programs that can perform symbolical algebraic calculations and handle complex matrices. Some popular options include Mathematica, Maple, and MATLAB. These programs have built-in functions for matrix operations and can handle abstract algebraic expressions as well. You can easily input your expression and get the result without having to do the calculation manually. I would suggest trying out different programs to see which one suits your needs and preferences the best.