107 citations · 551 across the 65 of their papers we have counts for
5 papers · 1 filter
Simple matrix models for the flag, Grassmann, and Stiefel manifolds
Lek-Heng Lim, Ke Ye
We derive three families of orthogonally-equivariant matrix submanifold models for the Grassmann, flag, and Stiefel manifolds respectively. These families are exhaustive -- every o…
Minimal equivariant embeddings of the Grassmannian and flag manifold
Lek-Heng Lim, Ke Ye
We show that the flag manifold , with Grassmannian the special case , has an -equivariant e…
Grassmannian optimization is NP-hard
Zehua Lai, Lek-Heng Lim, Ke Ye
We show that unconstrained quadratic optimization over a Grassmannian is NP-hard. Our results cover all scenarios: (i) when and are both allowed to…
Simple matrix expressions for the curvatures of Grassmannian
Zehua Lai, Lek-Heng Lim, Ke Ye
We show that modeling a Grassmannian as symmetric orthogonal matrices $\operatorname{Gr}(k,\mathbb{R}^n) \cong\{Q \in \mathbb{R}^{n \times n} : Q^{\scriptscriptstyle\mathsf{T}} Q =…
Degree of the Grassmannian as an affine variety
Lek-Heng Lim, Ke Ye
The degree of the Grassmannian with respect to the Plücker embedding is well-known. However, the Plücker embedding, while ubiquitous in pure mathematics, is almost never used in ap…