An algebraic condition for the separation of two ellipsoids

Given two ellipsoids, we show that their characteristic equation has at lea st two negative roots and that the ellipsoids are separated by a plane if a nd only if their characteristic equation has two distinct positive roots. F urthermore, the ellipsoids touch each other externally if and only if the c haracteristic equation has a positive double root. An advantage of this cha racterization is that only the signs of the roots matter. (C) 2001 Elsevier Science B.V. All rights reserved.