Geodesic
A new family of spectrally arbitrary ray patterns
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 4, pp. 1049-1058

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An $n\times n$ ray pattern $\mathcal {A}$ is called a spectrally arbitrary ray pattern if the complex matrices in $Q(\mathcal {A})$ give rise to all possible complex polynomials of degree $n$. \endgraf In a paper of Mei, Gao, Shao, and Wang (2014) was proved that the minimum number of nonzeros in an $n\times n$ irreducible spectrally arbitrary ray pattern is $3n-1$. In this paper, we introduce a new family of spectrally arbitrary ray patterns of order $n$ with exactly $3n-1$ nonzeros.
An $n\times n$ ray pattern $\mathcal {A}$ is called a spectrally arbitrary ray pattern if the complex matrices in $Q(\mathcal {A})$ give rise to all possible complex polynomials of degree $n$. \endgraf In a paper of Mei, Gao, Shao, and Wang (2014) was proved that the minimum number of nonzeros in an $n\times n$ irreducible spectrally arbitrary ray pattern is $3n-1$. In this paper, we introduce a new family of spectrally arbitrary ray patterns of order $n$ with exactly $3n-1$ nonzeros.
DOI : 10.1007/s10587-016-0309-3
Classification : 15A18, 15A29
Keywords: ray pattern; potentially nilpotent; spectrally arbitrary ray pattern 
Mei, Yinzhen; Gao, Yubin; Shao, Yanling; Wang, Peng. A new family of spectrally arbitrary ray patterns. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 4, pp. 1049-1058. doi: 10.1007/s10587-016-0309-3
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[4] Mei, Y., Gao, Y., Shao, Y., Wang, P.: The minimum number of nonzeros in a spectrally arbitrary ray pattern. Linear Algebra Appl. 453 (2014), 99-109. | MR | Zbl

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