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

Answer 2

By definition, by multiplying a 1D vector by its transpose, you've created a singular matrix.

Each row is a linear combination of the first row.

Notice that the second row is just 8x the first row.

Likewise, the third row is 50x the first row.

There's only one independent row in your matrix.