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We show that if a real $n\times n$ non-singular matrix ($n\ge m$) has all its minors of order $m-1$ non-negative and has all its minors of order $m$ which come from consecutive rows non-negative, then all $m$th order minors are non-negative, which may be considered an extension of Fekete’s lemma.

We show that each element in the semigroup $S_n$ of all $n\times n$ non-singular upper (or lower) triangular stochastic matrices is generated by the infinitesimal elements of $S_n$, which form a cone consisting of all $n\times n$ upper (or lower) triangular intensity matrices.