Multiplicative principal-minor inequalities for totally nonnegative matrices

An m-by-n matrix A is said to be totally nonnegative if every minor of A is nonnegative. Our main interest lies in characterizing all the inequalities that exist among products of principal minors of totally nonnegative matrices. We provide a complete description of all such inequalities for n-by-n totally nonnegative matrices with n=<5. Other general results are also proved including a characterization when detA[@a"1]detA[@a"2]=

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