python - Singular matrix issue with Numpy

Question

I am trying to multiply a vector(3 by 1) by its transpose(1 by 3). I get a (3 by 3) array but I cannot get its inverse. Any idea why?

import numpy as np

c=array([1, 8, 50])
np.transpose(c[np.newaxis]) * c
array([[   1,    8,   50],
   [   8,   64,  400],
   [  50,  400, 2500]])
np.linalg.inv(np.transpose(c[np.newaxis]) * c)
Traceback (most recent call last):
  File "<console>", line 1, in <module>
  File "C:Python26libsite-packages
umpylinalglinalg.py", line 445, in inv
    return wrap(solve(a, identity(a.shape[0], dtype=a.dtype)))
  File "C:Python26libsite-packages
umpylinalglinalg.py", line 328, in solve
    raise LinAlgError, 'Singular matrix'
LinAlgError: Singular matrix

question from:https://stackoverflow.com/questions/10326015/singular-matrix-issue-with-numpy

Answer 1

The matrix you pasted

[[   1,    8,   50],
 [   8,   64,  400],
 [  50,  400, 2500]]

Has a determinant of zero. This is the definition of a Singular matrix (one for which an inverse does not exist)

http://en.wikipedia.org/wiki/Invertible_matrix