MathDB
Classic - sum of rows and columns nonnegative

Source: 1961 All-Soviet Union Olympiad

August 4, 2015
combinatoricsinvariantmonovariantextremal principle

Problem Statement

Consider a table with one real number in each cell. In one step, one may switch the sign of the numbers in one row or one column simultaneously. Prove that one can obtain a table with non-negative sums in each row and each column.