Hi Gonzalo, Thanks for your comments.
On Jun 24, 8:06 am, Gonzalo Tornaria <[email protected]> wrote: > What's wrong with: Nothing - except there are no vector spaces in sight. I'd like to retain the exposure to vector spaces (eigenspaces) without going as far as Galois theory. They are a nice lead-in to invariant subspaces, which would be a central topic for a second course. > And what if the output of "B.eigenspaces_right()" is a bit confusing? > I'd argue that's actually a feature, because it will make the student > *think* about it, get a glimpse of some interesting mathematics, and > maybe open a door to a new world. I agree entirely with the sentiment. The students I teach have had a minimum of two semesters of calculus, and afterwards are expected to be ready for real analysis and abstract algebra. Many do not major in mathematics, but are from physics, computer science and economics. My course is different from many, in that we do not have an engineering college, so we don't serve that audience. I'll play the experience card - I've taught this course about 30 times. My experience tells me that if the only way to get an eigenspace of matrix over QQ is to take a detour into roots of irreducible polynomials, then I will just skip it entirely. It just goes too far down a road that I don't find beneficial for the vast majority of the students at that point - they are already struggling with ideas like matrix representations of linear transformations. With the Galois conjugate version optionally available, it will still be there via a keyword to challenge students (or inform our own research). I am just now about to implement optionally promoting a QQ matrix to a QQbar matrix when the eigenvalues lie outside QQ, to obtain an alternate format for output, as described above. I don't think there will be any disagreement with making that available. The question will be - what should the default be? So far, there is a +2\epsilon in favor of the QQbar version replacing the Galois conjugate version. Rob -- To post to this group, send an email to [email protected] To unsubscribe from this group, send an email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
