Generalizations of the Pfaffian to non-antisymmetric matrices
read the original abstract
We study two generalizations of the Pfaffian to non-antisymmetric matrices and derive their properties and relation to each other. The first approach is based on the Wigner normal-form, applicable to conjugate-normal matrices, and retains most properties of the Pfaffian, including that it is the square-root of the determinant. The second approach is to take the Pfaffian of the antisymmetrized matrix, applicable to all matrices. We show that this formulation is equivalent to substituting a non-antisymmetric matrix into the polynomial definition of the Pfaffian. We find that the two definitions differ in a positive real factor, making the second definition violate the determinant identity.
This paper has not been read by Pith yet.
Forward citations
Cited by 1 Pith paper
-
Interpolating non-Hermitian universality classes A and AI$^\dagger$: eigenvalue density and transition regime
Finite-N derivation of eigenvalue density in interpolating non-Hermitian ensemble reveals transitional edge regime at σ = 1 - κ N^{-1/2} conjectured to be universal.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.