From a definition of Principal minors :
Let A be a square matrix of dimension n. Let $\left[A\right]_{IJ}$ be the matrix consisting of only those rows in I⊂{1,…,n} and columns in J⊂{1,…,n}. If I=J≠∅, $\left[A\right]_{IJ}$ is called a principal minor.
There should be a $\left(_k^n\right)$ principal minors for a specific order k, and so $\sum _{k=1}^n\left(_k^n\right)$, but sometimes I read that there's $2^n-1$ principal minors.
Can anyone point to me to any reference to a proof