$M_{[i],[j]}=(-1)^{i_1+i_2+\cdots+i_k+j_1+j_2+\cdots+j_k}$, where $1\le i_1
By experiment in Maple for specific low-ish dimensional cases, all its eigenvalues are zero except for one, which takes the value $\left(n\atop k\right)$. What theorem or lemma can I cite to this effect for the general case, and in what book or paper?
This emerged in some Fermionic quantum field computations. All I really care about is whether this matrix is positive semi-definite, which it pretty clearly is from an experimental mathematics point of view and because of the antisymmetry, so if citing for positive semi-definiteness is easier, please feel free to do that instead.