On the superdeterminant function for supermatrices
N B Backhouse; A G Fellouris; N B Backhouse; Dept. of Appl. Maths. & Theoretical Phys., Univ. of Liverpool, Liverpool, UK; A G Fellouris; Dept. of Appl. Maths. & Theoretical Phys., Univ. of Liverpool, Liverpool, UK
Журнал:
Journal of Physics A: Mathematical and General
Дата:
1984-05-11
Аннотация:
A rigorous proof is given of the multiplicative property of the superdeterminant (Berezinian) of a supermatrix. The proof obviates the need to consider the domain of existence of the logarithm function for supermatrices, and devolves on the identity det(1-PQ) det(1-QP)=1, where P and Q are compatible rectangular matrices over the odd part of a Grassmann algebra.
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