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Tech. rep. UCL-INMA-2007.032 Continuous-time subspace flows related to the symmetric
 

Summary: Tech. rep. UCL-INMA-2007.032
Continuous-time subspace flows related to the symmetric
eigenproblem
P.-A. Absil
R. Mahony
R. Sepulchre§
28 July 2007
Abstract
The classes of continuous-time flows on Rn×p that induce the same flow
on the set of p-dimensional 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, finite-time 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 p-dimensional linear subspaces of Rn, and let span(Y ) Grass(p, n)

  

Source: Absil, Pierre-Antoine - Département d'ingénierie Mathématique, Université Catholique de Louvain

 

Collections: Mathematics