标题： 不变性和多项式恒等式对于高秩矩阵 显示英文标题

标题： Invariant and polynomial identities for higher rank matrices

摘要： 我们给出了秩较高的矩阵的判别式、行列式、特征多项式以及多项式恒等式的显式分量表达式。 我们定义了置换张量，并利用它们将判别式和行列式（作为阶数为$d$的判别式）构造出来，其中$d$是矩阵的维数。 由此得到了高秩矩阵的特征多项式和凯莱-哈密顿定理。 显示英文摘要

摘要： We exhibit explicit expressions, in terms of components, of discriminants, determinants, characteristic polynomials and polynomial identities for matrices of higher rank. We define permutation tensors and in term of them we construct discriminants and the determinant as the discriminant of order $d$, where $d$ is the dimension of the matrix. The characteristic polynomials and the Cayley--Hamilton theorem for higher rank matrices are obtained there from.