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Jul 12, 2020 at 14:52 comment added Bob Thank you! Given the gcd interpretation (thank you for altering me to that), It doesn't seem possible to find linear conditions so that the circulant matrix has rank $d-1$ provided $(v_1,\ldots, v_d)$ lies outside the resulting linear subspaces (that's really what I needed for my purposes)
Jul 12, 2020 at 5:53 vote accept Bob
Jul 12, 2020 at 5:40 history answered Gjergji Zaimi CC BY-SA 4.0