Python matrix inverse

I have a camera matrix k which I have computed. The value of k is:

[[  1.92160183e+08   0.00000000e+00   3.06056985e+02]
 [  0.00000000e+00   1.92160183e+08   1.57709172e+02]
 [  0.00000000e+00   0.00000000e+00   1.00000000e+00]]

Now, I have tried to find the inverse of k using numpy (using np.linalg.inv(k)). Let k1 be the inverse of k.

Using numpy, the value of k*k1 is:

[[  1.00000000e+00   0.00000000e+00  -4.87462472e-04]
 [  0.00000000e+00   1.00000000e+00  -1.29434633e-04]
 [  0.00000000e+00   0.00000000e+00   1.00000000e+00]]

Now, I was expecting a perfect identity matrix but since the values which should be zero are very small, I decided to ignore the fact that the result was not a perfect identity matrix.

Now my problem: I have two other matrices R and h. R is an identity matrix (it is not always an identity matrix but assume so for the sake of simplicity). I need to perform H1 = k*R*k1*h. This should ideally assign the value of h to H1 (since k*R*k1 should turn out to be identity).

My original h matrix:

 [[  1.71025842e+00  -7.51761942e-01   1.02803446e+02]
 [ -2.98552735e-16   1.39232576e-01   1.62792482e+02]
 [ -1.13518150e-18  -2.27094753e-03   1.00000000e+00]]

My R matrix:

[[ 1.  0.  0.]
 [ 0.  1. -0.]
 [-0.  0.  1.]]

The value of H1 produced using H1 = k*R*k1*h:

[[ 1.71025842 -0.         -0.        ]
 [-0.          0.13923258  0.        ]
 [ 0.         -0.          1.        ]]

The value of H1 produced using H1 = k*k1*h:

[[ 1.71025842 -0.         -0.05011282]
 [-0.          0.13923258 -0.02107099]
 [-0.         -0.          1.        ]]

Why is the value of H1 not coming equal to h as it should? How can I fix this?

Solution:

Your understanding on what the * operator does is flawed. It does not perform a dot product. But instead performs an elementwise multiplication on the two arrays, also known as the Hadamard product.

So, if you have two 2D matrices, A and B, the dot product is computed with –

enter image description here

Whereas, the hadamard product looks like this –

enter image description here

Which is an elementwise multiplication (and what you’re currently doing). Try replacing this with a call to np.ndarray.dot or using the @ operator:

>>> k.dot(k1)

Or,

>>> k @ k1   # python3.5+


array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]])

Contrast this with – 

>>> k * k1  
array([[  1.00000000e+00,   0.00000000e+00,  -4.87462473e-04],
       [  0.00000000e+00,   1.00000000e+00,  -1.29434634e-04],
       [  0.00000000e+00,   0.00000000e+00,   1.00000000e+00]])

Which is what you were getting earlier.