MathDB
Putnam 2005 A4

Source:

December 5, 2005
Putnamlinear algebramatrixinequalitiesvectorratioabsolute value

Problem Statement

Let HH be an n×nn\times n matrix all of whose entries are ±1\pm1 and whose rows are mutually orthogonal. Suppose HH has an a×ba\times b submatrix whose entries are all 1.1. Show that ab≤n.ab\le n.
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