 
Summary: Tech. rep. UCLINMA2007.032
Continuoustime subspace flows related to the symmetric
eigenproblem
P.A. Absil
R. Mahony
R. Sepulchre§
28 July 2007
Abstract
The classes of continuoustime flows on Rn×p that induce the same flow
on the set of pdimensional subspaces of Rn are described. The power
flow is briefly reviewed in this framework, and a subspace generaliza
tion of the Rayleigh quotient flow [Linear Algebra Appl. 368C, 2003,
pp. 343357] is proposed and analyzed. This new flow displays a prop
erty akin to deflation in finite time.
Key words. Matrix flows, subspace flows, power flow, Grassmann Rayleigh quotient flow,
principal component analysis, invariant subspace, finitetime deflation.
1 Introduction
Let Rn×p
, with p < n, denote the set of all n×p matrices with full column rank, let Grass(p, n)
denote the set of all pdimensional linear subspaces of Rn, and let span(Y ) Grass(p, n)
