Abstract
Starting from the expression for the superdeterminant of (xI - M), whereM 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 superdeterminant, we are able to construct polynomials of lower degree which are also shown to be annihilated by the supermatrix.
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Urrutia, L.F., Morales, N. An extension of the Ccayley-Hamilton theorem to the case of supermatrices. Lett Math Phys 32, 211–219 (1994). https://doi.org/10.1007/BF00750663
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DOI: https://doi.org/10.1007/BF00750663