Linear kernel matrix inversion

gistfile1.txt

>>> K = X.dot(X.transpose())
>>> K
array([[ 2,  3,  3,  5,  5,  6],
       [ 3,  5,  4,  8,  7,  9],
       [ 3,  4,  5,  7,  8,  9],
       [ 5,  8,  7, 13, 12, 15],
       [ 5,  7,  8, 12, 13, 15],
       [ 6,  9,  9, 15, 15, 18]])
>>> np.linalg.inv(K)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/Users/zacstewart/Code/kaggle_belkin/lib/python2.7/site-packages/numpy/linalg/linalg.py", line 445, in inv
    return wrap(solve(a, identity(a.shape[0], dtype=a.dtype)))
  File "/Users/zacstewart/Code/kaggle_belkin/lib/python2.7/site-packages/numpy/linalg/linalg.py", line 328, in solve
    raise LinAlgError('Singular matrix')
numpy.linalg.linalg.LinAlgError: Singular matrix
>>> np.linalg.pinv(K)
array([[ 0.00068587,  0.00102881,  0.00102881,  0.00171468,  0.00171468,
         0.00205761],
       [ 0.00102881,  0.12654321, -0.12345679,  0.12757202, -0.12242798,
         0.00308642],
       [ 0.00102881, -0.12345679,  0.12654321, -0.12242798,  0.12757202,
         0.00308642],
       [ 0.00171468,  0.12757202, -0.12242798,  0.12928669, -0.12071331,
         0.00514403],
       [ 0.00171468, -0.12242798,  0.12757202, -0.12071331,  0.12928669,
         0.00514403],
       [ 0.00205761,  0.00308642,  0.00308642,  0.00514403,  0.00514403,
         0.00617284]])