[SciPy-user] Bug in inverse matrixcalculation for "scipy_core-0.8.4.win32-py2.3.exe"
Fernando Perez
Fernando.Perez at colorado.edu
Wed Dec 14 15:05:18 CST 2005
Randewijk P-J <pjrandew at sun.ac.za> wrote:
> Now that you metion it... "sometimes" the inverse of some of my
> supposedly singular matrixes has "very large" values, because the
> determinant is actually not zero, but a "very small" value... e.g.
>
>
>>>>linalg.det(m)
>
> -1.5717747464951435e-006
Yup. Condition number and singularity are actually decoupled notions (to the
surprise of many, including myself when I learned it). You can have a
perfectly non-singular matrix with hideous condition number (making its
finite-precision inversion effectively impossible) and also near-singular
matrices which are well-conditioned, and hence perfectly easy to invert.
Golub's text has an excellent discussion of this topic, which should be
manadatory reading for anyone doing numerical linear algebra. The above
paragraph I wrote refers specifically to sec. 2.7.3 (p. 81) in the second
edition, which gives examples of both situations.
Cheers,
f
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