Determine if the determinant is exactly zero

Question

I have many 10 by 10 (0,1) -matrices, and I would like to determine which have the determinant exactly 0 (i.e., singular). Using scipy.linalg.det, I get a floating point number that I have to check to make sure it's close to zero. Is it possible to accurately perform the calculations so that I can be sure that I do not find false positives?

On the other hand, maybe there are some guarantees regarding the smallest eigenvalue that can be used to ensure that the floating point method never makes false positives?

Answer 1

, , . :

scipy.allclose(det, 0)

kwargs.

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( 10x10 0,1 ) .

, : 10- 0/1 "" , . "" ^† /, 0,1.

^† _{10- ;)}

Answer 2

, . 0 1, , , ( /// -1, 0 1, ).

0, .

, ( ) .

. , , .

EDIT: , , 0,1, . . , det(), , , , det (M) == 0.0 , .

Answer 3

, , . python

numpy.linalg.cond(x, p=None)

http://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.cond.html.

. , , .., , , . . scicomp stackexchange .

Answer 4

1 0, 1. , 0.

, -, sympy .

Answer 5

what about test batches during a game with arg tolerance, then select the maximum tolerance allowed, rinse and repeat: http://docs.scipy.org/doc/numpy/reference/generated/numpy.allclose.html