I’m trying to prove that the eccentricity of a conic doesn’t change through BAT (bijective affine transformations). It seems pretty obvious to me that by translations and rotations it won’t change. I can’t use the determinant of the projective matrix of the conic.
2026-03-25 18:49:08.1774464548
How can I prove the eccentricity of a quadratic conic is invariant under bijective affine transformations?
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You can't prove it because it's not true. Scaling $x$ by a factor of $2$ and leaving $y$ alone transforms a circle into an ellipse.