(this is in python 2.7.13)

If I have matrix A:

a =[[0,1,0,0,0,1],  [4,1,0,3,2,0],  [0,0,1,0,0,0],  [0,1,0,0,1,0],  [0,0,0,0,1,0],  [0,0,0,0,0,0],  
]

and a list of index's b =[0, 1, 3]

I would like to extract a smaller matrix from the matrix a using the index list b as the rows and columns.

So, it would be:

[0] row of matrix a; columns[0,1,3]
[1] row of matrix a; columns[0,1,3]
[3] row of matrix a; columns[0,1,3]

Which would equal, as example:

[[0,1,0], #0 row, 0,1,3 items[4,1,3], #1 row, 0,1,3 items[0,1,0]  #3 row, 0,1,3 items
]

You can do it by:

a =[[0,1,0,0,0,1],  [4,1,0,3,2,0],  [0,0,1,0,0,0],  [0,1,0,0,1,0],  [0,0,0,0,1,0],  [0,0,0,0,0,0],  
]b = [0, 1, 3]
c = [[a[i][j] for j in b] for i in b]
print(c)
# ===>
# [[0, 1, 0], [4, 1, 3], [0, 1, 0]]

(Anyway, Python2 is no longer supported: link. I recommend you use Python3+NumPy, which supports various matrix operations such as flexible indexing that you want.)