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 …

2021年10月1日 · 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 …

$\begingroup$ 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 …

2015年7月28日 · 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, …

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2018年11月28日 · The problem with defining the pfaffian of a matrix whose determinant is the square of the polynomial is ...

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2020年3月11日 · 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 …

2021年4月8日 · 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 …

2012年11月25日 · 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 …