Questions tagged [pfaffian]

The Ricci and scalar curvatures have very nice pointwise interpretations (using the local expression for the volume form for example). So, (at least Ricci) having special metrics (like Einstein) can ...

Let $n$ be a positive even integer. We introduce three types of skew-symmetric matrices, $A_{n+2}$, $B_n$ and $C_n$ (the subscript denotes the dimension of the matrices) in terms of the variables $z_1,...

Currently I'm reading "Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function" by Wilkie, and I do not ...

The identity $$\left| \begin{array}{cccc} x & y_1 & y_2 & y_3 \\ z_1 & 0 & a & b \\ z_2 & -a & 0 & c \\ z_3 & -b & -c & 0 \\ \end{array} \right|=\...

I've been struggling here to invert some integral equation involving Pfaffians, and it would be very nice if you could shed some light on the problem. Let's go to it. Let $V=\{-1,1\}^{m}$ and $S = \...