references:

https://cdn.vanderbilt.edu/vu-my/wp-content/uploads/sites/2392/2015/07/14141714/Tara-E-Fife.pdf

https://arxiv.org/abs/1606.08354

prove the exchange property

prove through induction on (use definition 1)

  • , this is obvious.
  • assume exchange property holds for . Need to prove that for two independent set , , s.t. . Suppose the exchange property doesn’t hold for . For all exists , . Since is an independent set, for those , , then for those . Thus for any , there is a set s.t. , and those are disjoint since . Thus . So exchange property holds for

一点点关于拟阵交和带权拟阵交的原始的想法：