An Extension of the Cayley-Hamilton theorem to the case of supermatrices

Urrutia, L.F.; Morales, N.

doi:10.1007/BF00750663

An Extension of the Cayley-Hamilton theorem to the case of supermatrices

L.F. Urrutia
(
- Mexico City U., Iztapalapa and
- CECS, Valdivia
)
,
N. Morales
(
- Mexico City U., Iztapalapa
)

1994

14 pages

Published in:

Lett.Math.Phys. 32 (1994) 211

e-Print:

hep-th/9609010 [hep-th]

DOI:

10.1007/BF00750663

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Abstract:

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 superdeterminant we are able to construct polynomials of lower degree which are also shown to be annihilated by the supermatrix.

Note:

14 pages, plain TEX

References(22)

Figures(0)

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