Singular Subspace Perturbation Bounds via Rectangular Random Matrix Diffusions

Peiyao Lai, Oren Mangoubi

Given a matrix $A\in {\mathbb{R}}^{m\times d}$ with singular values $\ddot{I}{ƒ}_1\ge \cdots \ge \ddot{I}{ƒ}_d$, and a random matrix $G\in {\mathbb{R}}^{m\times d}$ with iid $N(0,T)$ entries for som…