how to get the diagonal of a matrix?

edit

You could also do something like:

   sage: A=matrix(QQ,3,3,[3,-1,1,3,6,2,3,3,7]) 
   sage: A.numpy().diagonal() 
   array([3, 6, 7])

I don't believe so.

sage: [A[z][z] for z in range(A.nrows())]

[3, 6, 7]

could work. But I don't know that this is what you are looking for. Would you find this useful as an attribute? What output would be expected for a non-square matrix?

Depending on whether you want to do numerics or exact linear algebra, you can use Numpy/Scipy's matrix object. (Numpy and Scipy are included in Sage.) For example:

sage: import numpy as np
sage: A = np.matrix([[3,-1,1],[3,6,2],[3,3,7]])
sage: A.diagonal()
matrix([[3, 6, 7]])

The diagonal() method also supports rectangular matrices. It does the obvious, which is to continue down the diagonal until a "side" of the matrix is hit. For example, if I add a row to the above matrix I get the following output:

sage: B = np.matrix([[3,-1,1],[3,6,2],[3,3,7],[0,0,0]])
sage: B.diagonal()
matrix([[3, 6, 7]])

Or if I add a column at the end:

sage: C = np.matrix([[3,-1,1,0],[3,6,2,0],[3,3,7,0]])
sage: C.diagonal()
matrix([[3, 6, 7]])

But again, Numpy/Scipy's specialty is in floating point arithmetic. (I.e. numerics) Thankfully, there is a decent amount of compatibility between Numpy's numpy.matrix object and Sage's sage.matrix object.