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.
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 .
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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 
.