The John Theorem for Simplex
Si Lin, Xiong Ge, Leng Gangsong
TL;DR
This paper characterizes the John ellipsoid of a simplex, showing it is a ball if and only if the simplex is regular, and that for regular simplices, the John ellipsoid coincides with the inscribed ball.
Contribution
It provides a complete description of the John contact points for regular simplices and establishes a unique characterization of the John ellipsoid in this context.
Findings
The John ellipsoid of a regular simplex is its inscribed ball.
The John ellipsoid of any simplex is a ball if and only if the simplex is regular.
For regular simplices, the John ellipsoid coincides with the inscribed ball.
Abstract
In this paper, we give a description of the John contact points of a regular simplex. We prove that the John ellipsoid of any simplex is ball if and only if this simplex is regular and that the John ellipsoid of a regular simplex is its inscribed ball.
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Taxonomy
TopicsMathematics and Applications · Point processes and geometric inequalities · graph theory and CDMA systems