2007/01/31 by Victor Tapia, Víctor Tapia
Computer Science · Mathematics · Physics and Astronomy · #Algebra over a field #Characteristic polynomial #Combinatorics #Dimension (graph theory) #Discriminant #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Matrix Theory and Algorithms #Order (exchange) #Permutation (music) #Permutation matrix #Polynomial #Pure mathematics #Quantum Information and Cryptography #Rank (graph theory) #Tensor decomposition and applications #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/1751-8113/40/21/005
published as J. Phys. A: Math. Theor. 40, 5525 (2007)
arxiv created 2007/01/31 · openalex publication_date 2007/05/08 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.