Determinants of binomial-related circulant matrices
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Abstract Due to their rich algebraic structures and wide applications, circulant matrices have been of interest and continuously studied. In this paper, n×n complex left and right circulant matrices whose first row consists of the coefficients in the expansion of (x + zy)n−1 are focused on, where z is a nonzero complex number and n is a positive integer. In the case where z ∈ {1, −1, i, −i}, explicit formulas for the determinants of such matrices are completely determined. Known results on the determinants of binomial circulant matrices can be viewed as the special case where z = 1. Finally, some remarks and open problems are discussed.
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1992 ◽
Vol 53
(1)
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pp. 1-8
2021 ◽
Vol 14
(2)
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pp. 380-395
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2021 ◽
2019 ◽
Vol 108
(2)
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pp. 262-277
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