8 papers
Generalized matrix nearness problems II
Rongbiao Thomas Wang, Chi-Kwong Li, Lek-Heng Lim
Given a matrix , a matrix nearness problem seeks an that most closely approximates in the sense of minimizing under a variety of constraints on .…
Linear representations of manifolds
Rongbiao Thomas Wang, Lek-Heng Lim, Ke Ye
A finite-dimensional linear representation of a group or an algebra may be regarded as a map into a space of matrices, endowing abstract elements with coordinates, and encoding alg…
Special orthogonal, special unitary, and symplectic groups as products of Grassmannians
Lek-Heng Lim, Xiang Lu, Ke Ye
We describe a curious structure of the special orthogonal, special unitary, and symplectic groups that has not been observed, namely, they can be expressed as matrix products of th…
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…
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…