m = {{0, 0, 1, 0}, {0, 0, 0, 1}, {-5 X^2, X^2, 0, 0}, {X^2, -X^2, 0, 0}};
Simplify[Eigenvalues[m], Assumptions -> X>0]
The output I get is this below. The last two eigenvalues are not in their simplest form. They too are complex numbers.
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1 Answer
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2
I found a simple way:
Simplify[Eigenvalues[m], Assumptions -> X > 0] // PowerExpand
I think the function ComplexityFunction or function TransformationFunctions is likely to do the same, but I don't know how to do it yet.
answered Nov 11, 2020 at 3:56
A little mouse on the pampasA little mouse on the pampas
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1$\begingroup$ Shorter:
Simplify[Eigenvalues[m], X > 0] // PowerExpand$\endgroup$ Commented Nov 11, 2020 at 4:26 -
3$\begingroup$ Not the shortest, but there is a Wolfram Function Repository that can be of use once the eigenvalues are properly preprocessed:
Map[ResourceFunction["RadicalDenest"], PowerExpand[Factor[evals]]]$\endgroup$ Commented Nov 11, 2020 at 16:10