[Python] Is there a way to impose an ordering on eigenvalues from a parametrized matrix?

Discussão em 'Python' iniciado por Stack, Junho 13, 2025.

  1. Stack

    Stack Membro Participativo

    I have a 3x3 matrix, call it H, dependent on the parameters f, B. I then let f range from 0 to pi, and for each take the eigenvalues of H(f) using numpy's function: numpy.linalg.eig(). This gives me a list, and in the following plot I'm showing the first, second and third element of that list as red, blue and green resp.

    Clearly the eigenvalues depend continuously on f, so I'm sure there's some sense in which it's meaningful to say that all the points connected by a smooth curve are "the same" or "belong together". Numpy, however, yields the eigenvalues in an ordering that seems arbitrary and inconsistent, at least for my purposes.

    How would I go about recovering the ordering I'm alluding to above?

    Eigenvalues for a particular value of B Eigenvalues for a different value of B, in which two of the curves intersect

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