On sufficient conditions for the total positivity and for the multiple positivity of matrices

Olga M. Katkova, Anna M. Vishnyakova

The following theorem is proved: Suppose $M=(a_{i,j})$ be a $k\times k$ matrix with positive entries and $a_{i,j}a_{i+1,j+1} > 4\cos ^2 \fracπ{k+1} a_{i,j+1}a_{i+1,j} \quad (1 \…