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| Paper IPM / M / 2350 |
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| Abstract: | |||||||
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Let μm be the group of m-th 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.
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