A new family of spectrally arbitrary ray patterns

Yinzhen Mei; Yubin Gao; Yan Ling Shao; Peng Wang

Czechoslovak Mathematical Journal (2016)

  • Volume: 66, Issue: 4, page 1049-1058
  • ISSN: 0011-4642

Abstract

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An n × n ray pattern 𝒜 is called a spectrally arbitrary ray pattern if the complex matrices in Q ( 𝒜 ) give rise to all possible complex polynomials of degree n . In a paper of Mei, Gao, Shao, and Wang (2014) was proved that the minimum number of nonzeros in an n × n irreducible spectrally arbitrary ray pattern is 3 n - 1 . In this paper, we introduce a new family of spectrally arbitrary ray patterns of order n with exactly 3 n - 1 nonzeros.

How to cite

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Mei, Yinzhen, et al. "A new family of spectrally arbitrary ray patterns." Czechoslovak Mathematical Journal 66.4 (2016): 1049-1058. <http://eudml.org/doc/287583>.

@article{Mei2016,
abstract = {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 $n$. 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.},
author = {Mei, Yinzhen, Gao, Yubin, Shao, Yan Ling, Wang, Peng},
journal = {Czechoslovak Mathematical Journal},
keywords = {ray pattern; potentially nilpotent; spectrally arbitrary ray pattern; ray pattern; potentially nilpotent; spectrally arbitrary ray pattern},
language = {eng},
number = {4},
pages = {1049-1058},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A new family of spectrally arbitrary ray patterns},
url = {http://eudml.org/doc/287583},
volume = {66},
year = {2016},
}

TY - JOUR
AU - Mei, Yinzhen
AU - Gao, Yubin
AU - Shao, Yan Ling
AU - Wang, Peng
TI - A new family of spectrally arbitrary ray patterns
JO - Czechoslovak Mathematical Journal
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 4
SP - 1049
EP - 1058
AB - 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 $n$. 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.
LA - eng
KW - ray pattern; potentially nilpotent; spectrally arbitrary ray pattern; ray pattern; potentially nilpotent; spectrally arbitrary ray pattern
UR - http://eudml.org/doc/287583
ER -

References

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  1. Drew, J. H., Johnson, C. R., Olesky, D. D., Driessche, P. van den, Spectrally arbitrary patterns, Linear Algebra Appl. 308 (2000), 121-137. (2000) MR1751135
  2. Gao, Y., Shao, Y., New classes of spectrally arbitrary ray patterns, Linear Algebra Appl. 434 (2011), 2140-2148. (2011) Zbl1272.15019MR2781682
  3. McDonald, J. J., Stuart, J., Spectrally arbitrary ray patterns, Linear Algebra Appl. 429 (2008), 727-734. (2008) Zbl1143.15007MR2428126
  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. (2014) Zbl1328.15020MR3201687

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