The topic in class this week is abstract vector spaces. Sage does understand abstract vector spaces (and many other abstract algebraic structures) to some extent, but not in a way that is useful at the level of this class. So, here’s a brief discussion of creating matrices for computational practice. First, for row reduction practice, […]
Determinants in Sage work exactly how you would expect: M = matrix([[1,2,3],[4,5,6],[3,2,1]]) M.determinant() (If you’re surprised you got 0, check the RREF: M is, indeed, singular.) There are two shortcuts for the determinant, giving exactly the same thing: M.det() det(M) Go wild.
Amazingly, Sage knows what a linear subspace is, and can do basic computations with them. (Why is this amazing? This is a fairly abstract concept to implement on a computer. You can reduce most computations involving subspaces to computations about matrices. Usually, I would expect a human would do that reduction, and then ask a […]
Inverting matrices The first topic we discussed this week is inverting matrices. This works exactly as you would expect: M = matrix([[1,2,3],[1,1,1],[3,1,4]]) M.inverse() As a sanity check: M * M.inverse() (Note that the .inverse() comes first in the order of operations, as it should. If we didn’t know Python would do this way, we […]