# Plotting Ellipsoids with large weight matrix

I'm running into some problems plotting 2D Ellipsoids with non-diagonal weight matrices -- they are not centered where they are supposed to be. I'm not sure exactly what the problem is, it only seems to happen when the numbers are $\gg1$. The ellipse can even change positions if you change the plot range. The same thing happens with both Epilog and Show.

I am using version 10.0.2.0. Thanks for any help or workarounds. I am trying to plot ellipses corresponding to confidence regions on top of density plots, so the scales of the axes matter to me.

Row[
Plot[x, {x, -500, 500},
Epilog -> {Opacity[0], EdgeForm[Thick],
Ellipsoid[{0, 0},
RotationMatrix[#].{{40000, 0}, {0, 20000}}.RotationMatrix[-#]]},
AspectRatio -> 1, ImageSize -> 300
] & /@ {0, 10^-8, π/4}
]


Row[Plot[x, {x, -500, 500},

• I think there is may be some kind of bug. Consider Plot[x, {x, -500, 500}, Epilog -> {Rotate[ Ellipsoid[{0, 0}, {{4000, 0}, {0, 2000}}], \[Pi]/4]}, AspectRatio -> 1] When I plot this, and move the cursor up and down, the position of the ellipse seems to jump around. May 12, 2016 at 16:11
• To make your answer more general (in most practical cases the rotation matrix would not be explicitly there), something like makeEllipse[p_, mat_] := Module[{d, v}, {d, v} = Eigensystem[mat]; Rotate[Ellipsoid[p, Sqrt@d], ArcTan @@ (First@v)]] would be good. Thanks again, I will accept. May 12, 2016 at 16:15