On Jun 23, 5:35 pm, mmarco <[email protected]> wrote: > > Over R? Over C? > > From my limited experience in tutoring linear algebra to undergrads, I > > only saw confusion when > > eigenvalues were required to be in R. > > I would never go for this in any class I teach myself; I would always > > say that we allow any root of > > det(A-xI) to occur, not only real one. > > > Dima > > If you are talking about vector spaces over a field, what makes sense > is to consider only the eigenvalues that lie in that field. If you > talk about plain matrices, that's another stuff (the same matrix may > represent an endomorphism of different vector spaces). But considering > that in sage the matrices have a base ring, i don't consider the idea > of taking the eigenvalues in that same base ring to be stupid.
Given that we talk about A = matrix([[0,-1,0,0],[1,0,0,0],[0,0,0,-1],[0,0,1,0]]) # no field explicitly specified do you suggest that Sage should restrict itself to eigenvalues in Z, which is the base ring of A? Do you suggest that Sage should check whether we create a proper extension of a base ring when we adjoin a particular eigenvalue to it? Eigenvalues, without a specialization to a ring/field, are the roots of characteristic polynomial, that's it. One can introduce real, etc, eigenvalues, perhaps... -- 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
