Is there a software for symbolic manipulation that can treat matrices as whole variables?
For instance:
solve A = B + C * A for A
where A, B, C are matrices or vectors of generic size and possibly with given assumptions (like Hermitian, positive definite, singular, etc), but without knowing the exact dimensions and elements.
This should yield:
A = inv(I - C) * B
As far as I understand, applications like Sage, Matlab, Mathematica, SymPy, all treat matrices like sets of individual elements, but they do not truly implement matrix algebra. Am I wrong?
Sympy i think it is very promising. https://docs.sympy.org/latest/modules/matrices/expressions.html Edit: I didnt notice rodrigos comment.