※ 引述《KJLP (PWKJ)》之铭言： : 1)A is a k×k matrix all of whose entries are ±1 : and whose rows are mutually orthogonal. : Suppose that A has an m×n submatrix whose entries are all 1. : show that mn≦k. : 实在没头绪的一题 感觉应该是要利用A的每列orthogonal : 以及子矩阵每列相同这点? By condition, there are distinct rows v1,v2,..,vm of the form vi=(1,1,...,1, ui) --------- n then <vi,vj> = n + <ui,uj> = kd_ij, where d_ij=0 if i!=j, 1 if i=j. Taking sum over all 1<= i,j <=m, nm^2 + ||u1+..+um||^2 = km so nm^2 <= km, nm<=k. --

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