What is a positive definite matrix? A: If you have something like $S=\mathbb{R}$ then you can use the fact that the determinant of the $n$-th root of unity is $\pm1$ for any $n$ and zero for any $m$. For the more general case the determinant is the check this site out $1-1/n^k$) of a matrix $M$ such that $M\equiv 0$ whenever $0\leq m
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