# Complicated output from simple Eigenvalues problem

I have code that uses Eigenvalues on matrices of various sizes. But the output of what should be a very simple problem, namely finding the eigenvalue of a 1x1 matrix, is overly complicated.

Eigenvalues[{{1-(0.2494562342391921 Exp[-2(-0.2+x)^2]+0.769722872465748 Exp[-2x^2])/(1-x^2)}}]

returns

(3.28871*10^-17 E^(-2 (-0.2+x)^2-2 x^2) (2.3405*10^16 E^(2 (-0.2+x)^2)+7.58524*10^15 E^(2 x^2)-3.04071*10^16 E^(2 (-0.2+x)^2+2 x^2)+3.04071*10^16 E^(2 (-0.2+x)^2+2 x^2) x^2))/(-1.+x^2)

Where did those 10^-17 and 10^16 terms come from? Why can't it just give me

1-(0.2494562342391921 Exp[-2(-0.2+x)^2]+0.769722872465748 Exp[-2x^2])/(1-x^2)

?

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The eigencode probably tried to factor a symbolic expression. That gets dicey when there are approximate numbers involved. – Daniel Lichtblau Apr 25 '14 at 21:02
@DanielLichtblau: a nasty side-effect is that Chop produces zero while FullSimplify acts as desired. – Wouter Apr 26 '14 at 16:38
@Wouter I assure you that particular side effect has bitten me more times, and in more delicate places, than I can describe in this forum. – Daniel Lichtblau Apr 26 '14 at 19:57
@Wouter: Yes, the interaction with Chop is exactly why I asked. In the end, I now check for 1x1 matrix and not send it through Eigenvalues unnecessarily, which sidesteps this issue. – Chris K Apr 27 '14 at 14:00