I have been experimenting with large matrix inversions (have to inverse the whole matrix is my specific case) to check the runtime. It all works well until I tried to inverse a 50000 by 50000 matrix:

In [10]: A = np.eye(50000)

In [11]: A
Out[11]: 
array([[ 1.,  0.,  0., ...,  0.,  0.,  0.],
       [ 0.,  1.,  0., ...,  0.,  0.,  0.],
       [ 0.,  0.,  1., ...,  0.,  0.,  0.],
       ..., 
       [ 0.,  0.,  0., ...,  1.,  0.,  0.],
       [ 0.,  0.,  0., ...,  0.,  1.,  0.],
       [ 0.,  0.,  0., ...,  0.,  0.,  1.]])

In [12]: %time X = np.linalg.inv(A)
CPU times: user 2.95 s, sys: 3.24 s, total: 6.19 s
Wall time: 6.19 s

In [13]: X.shape
Out[13]: (50000, 50000)

In [14]: np.abs(X).sum()
Out[14]: 0.0

The run time of ~6 seconds is very small. But more importantly: I should not have the inv() function to return an all-zero matrix without any error!

Am I missing something here? Is it a result I should be expecting?

About my environment:

Right before running the snippet above, I made sure I had enough RAM:

$ cat /proc/meminfo | grep MemFree
MemFree:        138568436 kB

Running Conda 3.12.0 with:
numpy 1.9.2 py27_p0 [mkl]

OS: Linux seftrtools1 3.16.0-34-generic #47~14.04.1-Ubuntu SMP Fri Apr 10 17:49:16 UTC 2015 x86_64 x86_64 x86_64 GNU/Linux

$ python --version
Python 2.7.6

$ ulimit
unlimited