how to get the diagonal of a matrix?
Is there something like ?
sage: A = matrix(QQ,3,3,[3,-1,1,3,6,2,3,3,7])
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.
Asked: 2010-08-23 08:13:36 -0500
Seen: 2,717 times
Last updated: Aug 24 '10