I have been dealing with linear algebra problems of the form A = Bx in Python and comparing this to a colleague's code in MATLAB and Mathematica. We have noticed differences between Python and the others when B is a singular matrix. When using
numpy.linalg.solve() I throw a singular matrix error, so I've instead implemented
.pinv() (the Moore Penrose pseudo inverse).
I understand that storing the inverse is computationally inefficient and am first of all curious if there's a better way of dealing with singular matrices in Python. However the thrust of my question lies in how Python chooses an answer from an infinite solution space, and why it chooses a different one than MATLAB and Mathematica do.
Here is my toy problem:
B = np.array([[2,4,6],[1,0,3],[0,7,0]]) A = np.array([,,]) BI = linalg.pinv(B) x = BI.dot(A)
The answer that Python outputs to me is:
[[ 0.4] [ 1. ] [ 1.2]]
While this is certainly a correct answer, it isn't the one I had intended: (1,1,1). Why does Python generate this particular solution? Is there a way to return the space of solutions rather than one possible solution? My colleague's code returned (1, 1, 1) - is there a reason that Python is different from Mathematica and MATLAB?