You have 4 equations with 16 unknowns, so there are going to be a lot of solutions.

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Many SymPy functions struggle with M[i, j] construction which creates MatrixElement instead of an ordinary Symbol. I would use a Matrix filled with Symbols: M = sp.Matrix(sp.symarray('M', (4, 4))) sp.solve(a - M*b, list(M)) This returns {M_3_0: (-M_3_1*(a0 + a1 + a2 + a3) - M_3_2*a1 - M_3_3*(a1 + 2*a2 + 3*a3) + a0)/a0, M_2_0: (-M_2_1*(a0 + a1 + a2 + a3) - M_2_2*a1 - M_2_3*(a1 + 2*a2 + 3 *a3) + a1)/a0, M_1_0: (-M_1_1*(a0 + a1 + a2 + a3) - M_1_2*a1 - M_1_3*(a1 + 2 *a2 + 3*a3) + a2)/a0, M_0_0: (-M_0_1*(a0 + a1 + a2 + a3) - M_0_2*a1 - M_0_3 *(a1 + 2*a2 + 3*a3) + a3)/a0} which, as previously mentioned, is a lot of solutions. You can plug in some arbitrary numbers for the free variables here. On Saturday, March 10, 2018 at 7:38:00 AM UTC-5, Matthias Geier wrote: > > Dear list. > > I have this equation: > > a = M * b, > > where a and b are column vectors and M is a 4x4 matrix. > a and b consist of quite simple expressions, M is unknown: > > >>> import sympy as sp > >>> a0, a1, a2, a3 = sp.symbols('a:4') > >>> a = sp.Matrix([a3, a2, a1, a0]) > >>> b = sp.Matrix([a0, a3 + a2 + a1 + a0, a1, 3 * a3 + 2 * a2 + a1]) > >>> M = sp.MatrixSymbol('M', 4, 4) > >>> sp.Eq(a, M * b) > Eq(Matrix([[a3], [a2], [a1], [a0]]), M*Matrix([ > [ a0], > [a0 + a1 + a2 + a3], > [ a1], > [ a1 + 2*a2 + 3*a3]])) > > What's the most straightforward way to solve this for M? > > I have actually found a way, but it seems a bit non-obvious to me: > > >>> def get_value(i, j): > ... return b[i].as_coefficients_dict()[a[j]] > ... > >>> M_inv = sp.Matrix(4, 4, get_value) > >>> M_inv.inv() > Matrix([ > [ 2, -2, 1, 1], > [-3, 3, -2, -1], > [ 0, 0, 1, 0], > [ 1, 0, 0, 0]]) > > This is the solution I'm looking for, but I was hoping there is a > better way to get it. > Also, the way I did it I had to know that I could look for the inverse > and then undo the inverse afterwards, but I would prefer if there is a > solution without this manual step. > > Thanks in advance! > > cheers, > Matthias > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To post to this group, send email to sympy@googlegroups.com. Visit this group at https://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/2bf0325e-6eab-48f2-8299-e1df21998030%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.