Generalizations of the Pfaffian to non-antisymmetric matrices
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 squ...
Saved in:
| Main Author | |
|---|---|
| Format | Journal Article |
| Language | English |
| Published |
06.09.2022
|
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Summary: | 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. |
|---|---|
| DOI: | 10.48550/arxiv.2209.02578 |