2025/11/04 by Nesterenko, Yuri
#Combinatorics (math.CO) #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2511.02387
Taking the largest principal angle as the distance function between same dimensional nontrivial linear subspaces in \mathdsRn, we describe the class of subspaces deviating from all the coordinate ones by at least \arccos(1 / √(n)). This study compliments and is motivated by the long-standing hypothesis put forward in \citeGTZ1997 and essentially stating that so-defined distance to the closest coordinate subspace cannot exceed \arccos(1 / √(n)). In this context, the subspaces presented here claim to be the extremal ones. Realized as the star spaces of all nontrivial 2-connected series-parallel graphs with certain edge weights and arbitrary edge directions, the given subspaces may be of interest beyond numerical linear algebra within which the original problem was formulated.