Abstract. 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 terms of them we construct discriminants and the determinant as the discriminant of order d, where d is the dimension of the matrix. Analogues of the characteristic polynomials and the Cayley–Hamilton theorem are obtained therefrom for higher rank matrices.

PACS numbers: 02.10.Hh, 02.10.Yn

Mathematics Subject Classification: 15A24, 15A72

Print publication: Issue 21 (25 May 2007)
Received 7 September 2006, in final form 11 April 2007
Published 8 May 2007