Ellipsoids

Why

A $n$-dimensional generalization of an ellipse.¹

Definition

An ellipsoid (or hyperellipse or hyperellipsoid) is a set $E\subset {\mathsf{R}}^n$ for which there exists $A\in {\mathsf{R}}^{n\times n}$ positive definite satisfying

$$E=\left\{x\right|x^{\mathrm{\top }}Ax\le 1\}.$$

1. Future editions will expand. ↩︎