
Accession Number : AD0708502
Title : THE EIGENVECTORS OF A REAL SYMMETRIC MATRIX ARE ASYMPTOTICALLY STABLE FOR SOME DIFFERENTIAL EQUATION,
Corporate Author : CENTER FOR NAVAL ANALYSES ARLINGTON VA
Personal Author(s) : Saperstone,Stephen H.
Report Date : JUL 1970
Pagination or Media Count : 23
Abstract : Let A be a real symmetric n x n matrix. For each real unit vector x one computes numbers mu = mu(x) and sigma = sigma(x), which have the property that (mu + sigma, mu  sigma) contains an eigenvalue of A. An autonomous differential equation is established, dependent on A, which admits asymptotically stable solutions of the form, x = eigenvector of A. This is achieved by noting sigma squared (x) is a Liapunov function, and tends monotonically to zero along solutions of the differential equation. The set of critical points of sigma squared (x) are shown to comprise a finite union of products of spheres. (Author)
Descriptors : (*DIFFERENTIAL EQUATIONS, *MATRICES(MATHEMATICS)), STABILITY, THEOREMS
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE