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Keywords:
ray pattern; potentially nilpotent; spectrally arbitrary ray pattern
ray pattern; potentially nilpotent; spectrally arbitrary ray pattern
Summary:
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.
References:
[1] Drew, J. H., Johnson, C. R., Olesky, D. D., Driessche, P. van den: Spectrally arbitrary patterns. Linear Algebra Appl. 308 (2000), 121-137. MR 1751135
[2] Gao, Y., Shao, Y.: New classes of spectrally arbitrary ray patterns. Linear Algebra Appl. 434 (2011), 2140-2148. MR 2781682 | Zbl 1272.15019
[3] McDonald, J. J., Stuart, J.: Spectrally arbitrary ray patterns. Linear Algebra Appl. 429 (2008), 727-734. MR 2428126 | Zbl 1143.15007
[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 3201687 | Zbl 1328.15020
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