There is the possibility that this question may have been asked previously, but as we are unfamiliar with the nature of the chart below, we hope to seek a response to this query.
Consider a matrix as follows:
matrix = {{0.1 j, 0, 0, 0.2 j, 0}, {0, 0.1 j, 0, 0.2 j, 0}, {0, 0.1 j,
0, 0, 0.2 j}, {0.1 j, 0, 0, 0, 0.2 j}, {0, 0, 0.1 j, 0.2 j, 0}};
In any choice of j
which must be chosen in the range of [1,2,3,4]
, there is a set of eigenvalues (for this matrix we expect 5
eigenvalues for each j
separately), we are going to draw a chart similar to
in which the vertical axes shows eigenvalues magnitude (from the lowest one to the largest for various j's). (however the real eigenvalues are not 1, 2, 3
for j=1
for the above defined matrix the plot is just a schematic picture of what we wish to have). Also (for j=1 and j=2
) for instance there is a condition in which degeneracy is governed or the different between continuous eigenvalues for a special j
is less than 10^-3
, with a command same as:
Union[Eigenvalues[matrix] // N, SameTest -> (Abs[#1 - #2] < 10^-3 &)]
How we can draw this wish and with the last condition?