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On the matrices with constant determinant and permanent over roots of unity

Akbari, S ; Sharif University of Technology | 2003

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  1. Type of Document: Article
  2. DOI: 10.1016/S0024-3795(03)00659-1
  3. Publisher: 2003
  4. Abstract:
  5. Let μm be the group of mth roots of unity. In this paper it is shown that if m is a prime power, then the number of all square matrices (of any order) over μm with non-zero constant determinant or permanent is finite. If m is not a prime power, we construct an infinite family of matrices over μm with determinant one. Also we prove that there is no n×n matrix over μp with vanishing permanent, where p is a prime and n = pα-1. © 2003 Elsevier Inc. All rights reserved
  6. Keywords:
  7. Determinant ; Permanent ; Roots of unity
  8. Source: Linear Algebra and Its Applications ; Volume 375, Issue 1-3 , 2003 , Pages 245-249 ; 00243795 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0024379503006591