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

✍ Scribed by S. Akbari; H.-R. Fanaı̈; K. Mahmoudian

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 161 KB
• Volume: 375
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(03)00659-1

✦ Synopsis

Let µ m 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 µ m with non-zero constant determinant or permanent is finite. If m is not a prime power, we construct an infinite family of matrices over µ m with determinant one. Also we prove that there is no n × n matrix over µ p with vanishing permanent, where p is a prime and n = p α -1.