Matrix representation of an ellipse

Its nice to know how we can represent an ellipse and then an ellipsoid in the form of matrix. Such matrix represenation will help us develop various concepts of normal distribution while trying to fit an ellipse around datapoints.

 

I am placing this link here for reference.

 http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/geometry/simple.html