The Cayley-Hamilton theorem for supermatrices

Details The Cayley-Hamilton theorem for supermatrices The Cayley-Hamilton theorem for supermatrices

1993-04-22

arxiv.org/abs/gr-qc/9304036v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

ICN-UNAM-93-06, 34 pages

Scientific paper

10.1088/0305-4470/27/6/022

Starting from the expression for the superdeterminant of (xI-M), where M is an arbitrary supermatrix, we propose a definition for the corresponding characteristic polynomial and we prove that each supermatrix satisfies its characteristic equation. Depending upon the factorization properties of the basic polynomials whose ratio defines the above mentioned determinant we are able to construct polynomials of lower degree which are also shown to be annihilated by the supermatrix. Some particular cases and examples are considered.

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