Question

How do I calculate the middle eigenvalue in numpy?

Is this a correct way to do it?

import numpy as np

(1/a.ndim)*np.trace(a)

a is a numpy matrix.

Answer 1

That code will not calculate the middle eigenvalue for most definitions of the word “middle” (though it will work by chance on a 2×2 matrix).

If you want the mean of the eigenvalues (which is what the code you have written is closest to) then you could use:

import numpy as np
def mean_eigenvalue(a):
    return np.trace(a)/len(a)

assuming that a is an NxN matrix. This is because the trace is the sum of the eigenvalues, so if we divide by the size of the matrix (not its dimensionality, which should be two always) we get the mean.

If you want the median eigenvalue (which in the case where the matrix has an odd size is one of the eigenvalues; otherwise it is half way between two values) you can use:

import numpy as np
def median_eigenvalue(a):
    return np.median(np.linalg.eigvals(a))

Note that for 2×2 matrices these two values are the same.