Solution basis of underdetermined equation set in python

Question

I have an underdetermined equation set (m equations of n variables, m smaller than n). As such, if it is solvable then the set of solutions are a linear space (if it is a homogenic set) or affine space (non-homogenic).

Is there an easy way in Python (possibly with other libraries) to obtain this space - for example, a basis of which?

Thanks.

vartec · Answer 1 · 2009-03-02T11:07:24.533

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Use linalg package from SciPy

edited Mar 02 '09 at 11:07

answered Mar 02 '09 at 11:01

vartec

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My bad, I've pasted wrong link. See http://docs.scipy.org/doc/scipy/reference/linalg.html – vartec Mar 02 '09 at 11:09
scipy.linalg.orth ? Or better yet, ask this question on the SciPy list. – Andrew Dalke Mar 02 '09 at 12:20
Scroll down under "decompositions" and look at "svd" – duffymo Mar 02 '09 at 13:11
Sorry, look for svd on this link: http://wiki.aims.ac.za/mediawiki/index.php/Python:scipy_module:linalg#Decompositions. – duffymo Mar 02 '09 at 13:12

score 1 · Accepted Answer · answered Mar 02 '09 at 12:19

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Like the previous poster said, you'll want linalg from SciPy, but focus on the Singular Value Decomposition solution. The matrix U is the basis for the output vectors.

answered Mar 02 '09 at 12:19

duffymo

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I'm not sure I understand what you're suggesting. Trying `scipy.linalg.svd` for a few simple underdetermined inputs, the U matrix doesn't look anything like a basis for the solution set. Also, I don't see what you'd do for an inhomogeneous system. – user2357112 Oct 28 '16 at 00:17
It's actually the QR decomposition that's relevant here, not SVD. – KishKash Oct 02 '22 at 12:44

Solution basis of underdetermined equation set in python

2 Answers2