A null vector for the Rowland–Wu determinant identity

We prove the Rowland–Wu polynomial identity for every positive rectangular
matrix. The principal-minor coefficient sum is a single determinant. For a
matrix already scaled to row sums one and column sums $m/n$, that determinant
has an explicit null vector whose coordinate on a minor of order $k$ is
$(n/m)^k$. The proof is an elementary identity among minors of a Schur
complement, obtained by differentiating a determinant in four rank-one
directions. No nonvanishing-minor or genericity hypothesis is needed. We also
obtain explicit coefficients for arbitrary positive target margins and prove
their coefficient-sum and complementary-minor symmetries using the additive
compound of a rank-one matrix.