## IMC 2012 Problem 2

Let be a fixed positive integer. Determine the smallest positive rank of an matrix that has zeros along the main diagonal and strictly positive real numbers off the main diagonal.

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Let be a fixed positive integer. Determine the smallest positive rank of an matrix that has zeros along the main diagonal and strictly positive real numbers off the main diagonal.

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Hello,

This is one of problems that interests me. Have you the answer and can you share it please. Many thanks 🙂

It is easy to see that if then the rank of the matrix is at least . The main difficulty is to find an example of a matrix with rank exactly .