How to solve matrix equation with sympy?

Question

In sympy, given a matrix equation

M * x + N * y = 0 (or more complicated..)

how to solve this for x? (M,N = matrices, x,y = vectors)

I tried this with normal symbols, but obviously this failed. Using MatrixSymbol was not working as well. Is there some way to do it, or is sympy not capable of doing it?

Considered

Are the elements of M,N symbols or simply numbers? – Nerveless

the matrices M and N should not be defined by their elements, I'd just like to obtain the result x = M^-1 * ( - N * y ) – Considered

SymPy doesn't currently support solve on matrix expressions but it could if enough people ask for it. Perhaps you could raise an issue on github? github.com/sympy/sympy/issues – Sheffie

Answer 1

As MRocklin noted, MatrixExpressions don't support this yet, but noncommutative symbols do:

In [13]: M, N, x, y = symbols('M N x y', commutative=False)

In [15]: solve(M*x + N*y, x)
Out[15]:
⎡      -1⎤
⎣-N⋅y⋅M  ⎦

Unlike MatrixExpressions, noncommutative symbols don't have a notion of shape, so you'll need to keep track of that yourself. But this also shows that the basic things to implement this for MatrixExpression are already there. It will probably be easy to implement.

Armory

hmm, good but not good enough... Someone will have to implement the real thing... – Considered

As I said, it should be easy if you want to give it a shot. It should just be a matter of telling solve to treat matrix expressions the same as noncommutative symbols. – Armory

If I am not mistaken, the result of solve(M*x + N*y, x) should be $-M^{-1} N y$. – Centralize

Opened a new issue, "solve(Mx + Ny, x) fails for non-commutative symbols": github.com/sympy/sympy/issues/12258 – Centralize