Let $A$ be an skew symmetric [square matrix](Matrices.md#Square%20matrices) with real elements, the _Pfaffian_ is a real polynomial, $p(x)$ that comes from the [determinant](Determinants.md) of $A$ such that $p(\alpha x)=\alpha^{n/2}p(x)$ and $\det{A}=p^2(x_A)$ where $x_A$ are elements of $A.$ %%pg 259 of Bernstein's Matrix Mathematics - expand this entry based on that book.%% #MathematicalFoundations/Algebra/AbstractAlgebra/LinearAlgebra/Matrices