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