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 | 1 | initial version |
If I am understanding your question correctly - if you put the additional constraint of getting $x$ with the minimum norm, then you are asking for the Moore-Penrose pseudoinverse. In Sage you can explicitly call the pseudoinverse function of numpy
sage: MN = M.numpy()
sage: import numpy
sage: x = matrix(numpy.linalg.pinv(MN))*v
| | 2 | No.2 Revision |
If I am understanding your question correctly - if you put the additional constraint of getting $x$ with the minimum norm, then you are asking for the Moore-Penrose pseudoinverse. In Sage you can explicitly call the pseudoinverse function of numpy
sage: MN = M.numpy()
sage: import numpy
sage: x = matrix(numpy.linalg.pinv(MN))*v
Edit: Even the command
sage: x = M \ v
works for a nonsquare matrix M. But I am not sure what this is actually doing for a nonsquare matrix. The documentation does not seem to explain.
| | 3 | No.3 Revision |
If I am understanding your question correctly - if you put the additional constraint of getting $x$ with the minimum norm, then you are asking for the Moore-Penrose pseudoinverse. In Sage you can explicitly call the pseudoinverse function of numpy
sage: MN = M.numpy()
sage: import numpy
sage: x = matrix(numpy.linalg.pinv(MN))*v
Edit: Even the command
sage: x = M \ v
works for a nonsquare matrix M. But I am not sure what this is actually doing for a nonsquare matrix. The documentation does not seem to explain.explain. The solution obtained is not the same as obtained from the pseudoinverse.
