Appendix

Section A provides a proof that isometry preserves angles. Section D lists the grid considered for hyper-parameters. T is an isometry iff it preserves inner products. Suppose T is an isometry. Conversely, if T preserves inner products, then nullT (v w),T ( v w) null = null v w,v w null, which implies null T ( v w)null = null v w null, and since T is linear, nullT (v) T ( w) null = null v w null .