[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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