On the characteristic polynomial of supermatrices
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We prove that the coefficients of the so-called right 2-characteristic polynomial of a supermatrix over a Grassmann algebraG=G 0⊕G 1 are in the even componentG 0 ofG. As a consequence, we obtain that the algebra ofn×n supermatrices is integral of degreen 2 overG 0.
KeywordsCharacteristic Polynomial Grassmann Algebra Central Polynomial Nilpotent Ring Hamilton Identity
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- [D] M. Domokos,Cayley-Hamilton theorem for 2 × 2 matrices over the Grassmann algebra, Journal of Pure and Applied Algebra (1998), to appear.Google Scholar