홈 editorial content online
Volume 14 (2012)
No 1
Volume 13 (2011)
No 1
Volume 12 (2010)
No 1
Volume 11 (2009)
No 1, No 2
Volume 10 (2008)
No 1, No 2
Volume 9 (2006)
No 1, No 2
Volume 8 (2005)
No 1, No 2
Volume 7 (2004)
No 1, No 2
Volume 6 (2003)
No 1, No 2
Volume 5 (2002)
No 1, No 2
Volume 4 (2001)
No 1, No 2
Volume 3 (2000)
No 1
Volume 2 (1999)
No 1
Volume 1 (1998)
No 1

(1999 / vol.2 / no.1)
Fritz John's Convexity Theorem and Discrete Dynamics
Mau-Hsiang Shih
Pages. 66-68     



We consider the result of great impact by Fritz John in his work
on Convex Geometry. John showed in 1948 that the boundary of any convex
region centrally symmetric with respect to a point in ${f R}^n$ lies between two
concentric homothetic ellipsoids of ratio $1/sqrt{n}$. This result has become very
important for Geometric Algorithms. The purpose of this talk is to discuss its
matrix-theoretic version and its new application to Discrete Dynamics. The
content is mainly taken from papers : T. Ando and M. -H. Shih, SIAM J. Matrix
Anal (1998) ; M. -H. Shih, Linear Algebra Appl. (1999).



1. Fritz John's convexity theorem
2. Matrix-theoretic version
3. Nonautonomous Lyapunov inequalities



convex geometry, homothetic ellipsoids, geometric algorithms, discrete dynamics, Lyapunov ineualities, gelfand spectral radius formula



46A55, 52A07