Oct 1, 2021 · Now since the last term dominates the negative term, thanks to the superincreasing property of the sequence, the pfaffian is positive. What I am hoping is that finding a dominating …

Here is an approach using (possibly complex) Grassmann variables and Berezin integration $^1$ to prove the required relation $${\rm Det}(A)~=~{\rm Pf}(A)^2. \tag{1}$$ This approach isn't …

$\begingroup$ I found some literature on Pfaffian sums. Check for instance the series of three articles by M. Ishikawa, S. Okada and M. Wakayama entitled Applications of Minor-Summation …

Jul 28, 2015 · The Pfaffian is an invariant of matrices, but not of underlying linear operators. Two skew-symmetric matrices that are similar can have different Pfaffians: for example, …

Nov 28, 2018 · The problem with defining the pfaffian of a matrix whose determinant is the square of the polynomial is ...

Mar 11, 2020 · I would count this proof as very geometric, since the actual definition of Pfaffian (of a linear operator) depends on understanding the interaction between the orthogonal structure …

Nov 25, 2012 · The sign convention for the Pfaffian of a skew-symmetric matrix on the Wikipedia looks like the negative of the sign convention in Lang's Algebra (at least looking at the 4 by 4 …

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May 31, 2017 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …

Apr 8, 2021 · This is a guess but is founded in the similar logic used to find integrating factors for 2D Pfaffian equations, and this is the bit that I'm having trouble proving in general. From there, …