Victor Tapia 2007 J. Phys. A: Math. Theor. 40 5525 doi:10.1088/1751-8113/40/21/005
Victor Tapia
Show affiliationsWe 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.
15A72 Vector and tensor algebra, theory of invariants (See also 13A50, 14L24)
15A15 Determinants, permanents, other special matrix functions (See also 19B10, 19B14)
Issue 21 (25 May 2007)
Received 7 September 2006, in final form 11 April 2007
Published 8 May 2007
Victor Tapia 2007 J. Phys. A: Math. Theor. 40 5525
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