[HEOI2013] Calcium iron Zinc Selenium Vitamin __ Linear correlation

Description

Given the 2N 2N line vector A1,..., an,b1,..., BN a_1,\dots,a_n,b_1,\dots,b_n, a replacement scheme is needed, Ai a_i is replaced by Bj B_j (i∈[1,n],j∈[n+1,2n)) (i\in[1,n],j\ IN[N+1,2N]), each J J can only be used once. The requirement is that after each Ai a_i is replaced by the corresponding Bj B_j, the Ak (1≤k≤n) a_k (1\le k\le N) is linearly independent. and the dictionary order of the scheme is minimum. Announcement

My linear correlation knowledge is limited, this article only makes the qualitative analysis. Analysis

The A,b,c A,b,c mentioned later will be the matrix of NxN n\times N, where A is n n Ai a_i, and b b is the same. S-S Collection

First of all, the topic should be that a a must be linearly independent, otherwise the output is not appropriate (the explanation is unclear).

Then for each Bj B_j, a A can only have a minimum set S S, which satisfies S-linear independence, but joins B