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For the sake of simplicity, in the sequel a (Laurent) polynomial of negative degree is understood to be the zero polynomial and, similarly, a banded matrix with negative bandwidth reduces to the zero matrix.
A zero has a multiplicity, which refers to the number of times that its associated factor appears in the polynomial. For instance, the quadratic (x + 3)(x  2) has the zeroes x = 3 and x = 2, each occuring once.