We give simple formulas for the canonical metric, gradient, Lie derivative, Riemannian connection, parallel translation, geodesics and distance on the Grassmann manifold of p-planes in Rn. In theseâ€¦ (More)

Formulas are derived for the probability density function and the probability distribution function of the largest canonical angle between two p-dimensional subspaces of Rn chosen from the uniformâ€¦ (More)

We address the numerical problem of recovering large matrices of low rank when most of the entries are unknown. We exploit the geometry of the low-rank constraint to recast the problem as anâ€¦ (More)

In this paper, we present a retraction-based Riemannian BFGS approach (RBFGS). Of particular interest is the choice of transport used to move information between tangent spaces and the different waysâ€¦ (More)

2009 IEEE/SP 15th Workshop on Statistical Signalâ€¦

2009

This paper deals with the Riemannian geometry of the set of symmetric positive semidefinite matrices of fixed rank. This set is studied as an embedded submanifold of the real matrices equipped withâ€¦ (More)

We consider two Riemannian geometries for the manifold M(p,mÃ— n) of all m Ã— n matrices of rank p. The geometries are induced on M(p,mÃ— n) by viewing it as the base manifold of the submersion Ï€ :â€¦ (More)

This paper considers the connection between the intrinsic Riemannian Newton method and other more classically inspired optimization algorithms for equality-constrained optimization problems. Weâ€¦ (More)

A novel matrix flow for principal or minor component analysis is constructed. The development is based on decompositions of the set of full-rank nÃ— p matrices into orbits of Lie group actions.

We consider the problem of approximating a multiple-input multiple-output (MIMO) pÃ—m rational transfer function H(s) of high degree by another pÃ—m rational transfer function b H(s) of much smallerâ€¦ (More)

A numerical algorithm is proposed for computing an extreme eigenpair of a symmetric/positive-definite matrix pencil (A,B). The leftmost or the rightmost eigenvalue can be targeted. Knowledge of (A,B)â€¦ (More)