Let $A$ be a $n\times n$ real matrix.
If all the sub-determinant of $A$ is $\geq0$, then $A$ is called totally non-negative.
If all the sub-determinant of $A$ is $>0$, then $A$ is called totally positive.
If for a totally non-negative matrix $A$, there exists a positive integer $m$ such that $A^m$ is totally positive, then $A$ is called an oscillation matrix.
Prove that if $A$ is an oscillation matrix, then $A^{n-1}$ is totally positive...
I have no ideas...my god.
