5 papers · 1 filter
The eigenvalue decomposition of normal matrices by the skew-symmetric part
Simon Mataigne, Kyle A. Gallivan
We propose a new method for computing the eigenvalue decomposition of a dense real normal matrix through the decomposition of its skew-symmetric part. The method relies on algo…
Bounds on the geodesic distances on the Stiefel manifold for a family of Riemannian metrics
Simon Mataigne, P. -A. Absil, Nina Miolane
We give bounds on geodesic distances on the Stiefel manifold, derived from new geometric insights. The considered geodesic distances are induced by the one-parameter family of Riem…
The Selective G-Bispectrum and its Inversion: Applications to G-Invariant Networks
Simon Mataigne, Johan Mathe, Sophia Sanborn +2
An important problem in signal processing and deep learning is to achieve \textit{invariance} to nuisance factors not relevant for the task. Since many of these factors are describ…
An efficient algorithm for the Riemannian logarithm on the Stiefel manifold for a family of Riemannian metrics
Simon Mataigne, Ralf Zimmermann, Nina Miolane
Since the popularization of the Stiefel manifold for numerical applications in 1998 in a seminal paper from Edelman et al., it has been exhibited to be a key to solve many problems…
The ultimate upper bound on the injectivity radius of the Stiefel manifold
P. -A. Absil, Simon Mataigne
We exhibit conjugate points on the Stiefel manifold endowed with any member of the family of Riemannian metrics introduced by Hüper et al. (2021). This family contains the well-kno…