#11248: SVD matrix decomposition may return a non-invertible "unitary" matrix
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Reporter: rbeezer | Owner: jason, was
Type: defect | Status: new
Priority: major | Milestone: sage-4.7
Component: linear algebra | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Comment(by slabbe):
I ran the one-liner test a little bit more systematically. It all depends
on
the dimensions: 4 x 8 always work and 4 x 5 never work. For i,j < 10, here
are
the dimensions i x j that never work : 3 x 4, 4 x 5, 5 x 6, 5 x 7, 6 x 7,
6 x
8, 6 x 9, 7 x 8, 7 x 9, 8 x 9. Hence, the smallest examples I can get are
dimension 3 x 4. Here are some of them even if listing them is stupid
since
it looks to be broken for every 3 x 4 matrices:
{{{
[
[ 2*I - 2 -6*I + 1 I + 1 1]
[ -1 I + 1 -2*I 2]
[ -101 -I - 1 3*I 1],
[-2*I - 5 -I 2*I -3*I + 1]
[ 5 -3*I + 1 -I - 1 0]
[ -I - 1 I I -I],
[-5*I + 3 -I + 1 0 2*I + 8]
[ I -I I + 1 I - 1]
[ 2*I + 1 0 I + 4 -I],
[-2*I - 2 -I + 2 -I -I + 14]
[ -I - 2 15 -I + 1 2*I - 3]
[14*I - 1 2*I -I + 169 -I],
[-2*I - 5 10 -3*I -I - 19]
[ I - 2 2*I - 4 -I - 1 -I + 1]
[ -I - 3 -3*I - 1 -2 I + 1]
]
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11248#comment:8>
Sage <http://www.sagemath.org>
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