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Question: Non-commutative matrices

Question:Non-commutative matrices

Art Kalb 252 Maple 2025
linear-algebra abstract noncommutative-product physics blockmatrix
June 02 2025
3

I have a symbolic block matrix equation that I am trying to solve. Maple doesn't respect non-commutativity when solving.

I've tried to use 'Matrix' assumptions. I've also tried using the Physics package's Setup(noncommutativeprefix).

Both of these do not respect the order of multiplications (even using the dot operator for multiplication).

I've posted a minimal example below.

with(Physics)

Setup(noncommutativeprefix = {v, y})

[noncommutativeprefix = {v, y}]

 (1)

NULL``

expr := y__xx.v__x = y__xu.y__uu.v__u

y__xx*v__x = y__xu*y__uu*v__u

 (2)

soln := solve(expr, [v__u])

[[v__u = y__xx*v__x/(y__uu*y__xu)]]

 (3)

op(rhs(soln[][]))

y__xx, v__x, 1/y__uu, 1/y__xu

 (4)

NULL

Download noncommutative_example.mw

Does anyone know of a way to make this come out in a sensible fashion?
Thanks for the help!
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