标题： 凯莱-哈密顿定理到超矩阵情况的扩展 显示英文标题

标题： An extension of the Cayley-Hamilton theorem to the case of supermatrices

摘要： 从超行列式的表达式$ (xI-M)$开始，其中$M$是一个任意的超矩阵，我们提出了对应特征多项式的定义，并证明每个超矩阵都满足其特征方程。 根据定义上述超行列式的基本多项式比值的分解性质，我们能够构造出次数较低的多项式，并且这些多项式也被证明被超矩阵所消去。 显示英文摘要

摘要： 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.