Upper Bounds for the Distance to Finite-Dimensional Subspaces in Inner Product Spaces

$s$-距离子空间的上界

Upper Bounds for $s$-Distance Subspaces

本文将等角子空间研究扩展到$s$-距离子空间，建立其最大基数上界，推广并改进了Balla和Sudakov的相关结果。

Blade Products and the Angle Bivector of Subspaces

Principal angles are used to define an angle bivector of subspaces, which fully describes their relative inclination. Its exponential is related to the Clifford geometric product of blades, gives rotors connecting subspaces via minimal geodesics in Grassmannians, and decomposes giving Plücker coordinates, projection factors and angles with various subspaces. This leads to new geometric interpretations for this product and its properties, and to formulas relating other blade products (scalar, inner, outer, etc., including those of Grassmann algebra) to angles between subspaces. Contractions are…

Improving bounds for the Perel'man-Pukhov quotient for inner and outer radii

In this work we study upper bounds for the ratio of successive inner and outer radii of a convex body K. This problem was studied by Perel'man and Pukhov and it is a natural generalization of the classical results of Jung and Steinhagen. We also introduce a technique which relates sections and projections of a convex body in an optimal way.

等倾等倾子空间的维度计数界

Dimension-counting bounds for equi-isoclinic subspaces

该研究提出了等倾等倾子空间理论中的四个新贡献，包括块相干性的下界、偶维子空间的计数、数量上界以及在特定条件下进一步细化的证明。