吉澤真太郎 (Wuerzburg Univ., Germany)
Component Extraction Flows and Double Bracket Flows
We discuss a novel perspective between extraction of invariant subspace for a symmetric positive definite matrix and Hamiltonian systems. The motivation occures from triple directions.
The first is the geometry of Hamiltonian flows on homogeneous spaces disccussed by Thimm(1981), Bloch-Brockett-Crouch(1997), Bloch-Krishnaprasad-Marsden-Ratiu(1996).
The second comes from the information processing systems, in where Neural Network scientist are discussing the principal and minor component analysis, and also independent component analysis.
The third is NON-convex duality theory discussed by Ekeland (1977).
In this talk, I try to explain that the Legendre duality plays an important role between non-constrained optimization and constrained optimization in view of nonlinear dynamical systems including double bracket systems with “deformation” parameters. From this trick we can see a kind of the phase space compactification for the dynamical systems.