I have a $3 \times 3$ matrix which I define like so :
F = {{ω^2 + 1/2
\!\(\*SubsuperscriptBox[\(ω\), \(z\), \(2\)]\) (1 + \
ϵ), -I ω Subscript[ω, c] Cos[θ],
I ω Subscript[ω, c]
Sin[θ] Sin[ϕ]}, {I ω Subscript[ω, c]
Cos[θ], ω^2 + 1/2
\!\(\*SubsuperscriptBox[\(ω\), \(z\), \(2\)]\) (1 - \
ϵ), -I ω Subscript[ω, c]
Sin[θ] Cos[ϕ]}, {-I ω Subscript[ω, c]
Sin[θ] Sin[ϕ],
I ω Subscript[ω, c]
Sin[θ] Cos[ϕ], ω^2 -
\!\(\*SubsuperscriptBox[\(ω\), \(z\), \(2\)]\)}};
And I want to determine the Eigenvalues
of this matrix, I do this with:
Eigenvalues[F, Cubics -> True]
This works fine and I get the three eigenvalues, however if you run this code you will note that the eigenvalues are rather unpleasant. There are also some common factors that appear in all three of the equations.
I was wondering if there is a way I can either simplify these (using FullSimplify[...]
does not work it just runs continuously) or use Replace[...]
some how to just put the common factors into a constant and make the equations nicer this way.
Any ideas?