Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4599564 | Linear Algebra and its Applications | 2014 | 11 Pages |
A ray pattern AA is spectrally arbitrary if given any monic polynomial r(x)r(x) of order n with complex coefficients, there exists B∈Qr(A)B∈Qr(A) such that the characteristic polynomial of B is r(x)r(x). In [1], the authors first presented that a family of n×nn×n irreducible ray patterns with exactly 3n nonzeros is spectrally arbitrary. Then they proved that every n×nn×n irreducible spectrally arbitrary ray pattern has at least 3n−13n−1 nonzeros. So as pointed in [1], the minimum number of nonzeros in an n×nn×n irreducible spectrally arbitrary ray pattern is either 3n or 3n−13n−1.In this paper, we provide an irreducible spectrally arbitrary ray pattern of order n with 3n−13n−1 nonzeros. So the minimum number of nonzeros in an n×nn×n irreducible spectrally arbitrary ray pattern is 3n−13n−1.