Mike, "Right eigenvectors" should be column vectors placed on the right side of the matrix. The output is a triple for each eigenvalue: eigenvalue first, then a list of eigenvectors. While the eigenvectors print as rows, they will behave like columns when you want them to. Indexing into the output just takes some thought:
sage: spectrum = M.eigenvectors_right() sage: evalue = spectrum[0][0] sage: evector = spectrum[0][1][0] sage: M*evector-evalue*evector (-3.33066907388e-16 + 9.47634626984e-17*I, 5.55111512313e-17) So for the first eigenvalue, the output (up to rounding-off) is the zero vector, as expected if the items are really an eigenvalue and right eigenvector of M. Rob On Jun 5, 7:03 pm, Mike Witt <msg...@gmail.com> wrote: > I'm confused about this, and hoping for some clarification ... > > sage: M=matrix([[0, .707-.707*i],[.707+.707*i, 0]]) > sage: M = M.change_ring(CDF) > sage: M > [ 0 0.707 - 0.707*I] > [0.707 + 0.707*I 0] > sage: M.eigenvectors_left() > ([0.999848988598 + 5.55111512313e-17*I, -0.999848988598 - > 5.55111512313e-17*I], [0.707106781187 0.5 + 0.5*I] > [0.707106781187 -0.5 - 0.5*I]) > sage: M.eigenvectors_right() > ([0.999848988598 + 5.55111512313e-17*I, -0.999848988598 - > 5.55111512313e-17*I], [0.707106781187 0.707106781187] > [ 0.5 + 0.5*I -0.5 - 0.5*I]) > > I believe that eigenvectors_left() is giving me the answers that > I expected. But I don't understand the values returned by > eigenvectors_right(). > I *thought* that eigenvectors_right() was the one I wanted to call in > order > to get "regular old eigenvectors" (as a mathematical novice such as > myself > would be expecting to see). > > Thanks, > > -Mike -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
