 Ellipsoid

An ellipsoid is a level set $(x-c{)}^{T}A(x-c)=1$ for a real symmetric positive-definite matrix $A$. Its principal axes are the orthonormal eigenvectors of $A$, and an eigenvalue $\lambda$ gives semi-axis length $1/\sqrt{\lambda }$.

An ellipsoid is a three-dimensional geometric shape that is a generalized form of an ellipse. It is defined mathematically as the set of points in three-dimensional space that are a constant distance from a central point, but in this case, the distance is scaled differently along different axes.