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:\Python26\lib\site-packages\numpy\linalg\linalg.py", line 445, in inv

    return wrap(solve(a, identity(a.shape[0], dtype=a.dtype)))

  File "C:\Python26\lib\site-packages\numpy\linalg\linalg.py", line 328, in solve

    raise LinAlgError, 'Singular matrix'

LinAlgError: Singular matrix

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

To know more about this you can have a look at the following video:-