There are two approaches for indexing dense and sparse matrices: single-argument indexing and double-argument indexing.

In double-argument indexing a matrix is indexed using two index-sets I and J,

>>> from cvxopt.base import matrix
>>> A = matrix(range(16),(4,4))
>>> print A
[  0   4   8  12]
[  1   5   9  13]
[  2   6  10  14]
[  3   7  11  15]

>>> print A[[0,1,2,3],[0,2]]
[  0   8]
[  1   9]
[  2  10]
[  3  11]

The index-sets can be integers, lists, integer matrices, or slices:

>>> print A[1,:]
[  1   5   9  13]

>>> print A[::-1,::-1]
[ 15  11   7   3]
[ 14  10   6   2]
[ 13   9   5   1]
[ 12   8   4   0]

In single-argument indexing a matrix is indexed in vector-form by considering the matrix in column-major order (i.e., by stacking the columns from left to right).

>>> A[::5] = -1
>>> print A
[ -1   4   8  12]
[  1  -1   9  13]
[  2   6  -1  14]
[  3   7  11  -1]

This is useful for accessing parts of matrix that are not sub-matrices, e.g., the diagonal part of a matrix.