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

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