Some properties complementary to Brualdi-Li matrices

Chuanlong Wang; Xuerong Yong

Czechoslovak Mathematical Journal (2015)

  • Volume: 65, Issue: 1, page 135-149
  • ISSN: 0011-4642

Abstract

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In this paper we derive new properties complementary to an 2 n × 2 n Brualdi-Li tournament matrix B 2 n . We show that B 2 n has exactly one positive real eigenvalue and one negative real eigenvalue and, as a by-product, reprove that every Brualdi-Li matrix has distinct eigenvalues. We then bound the partial sums of the real parts and the imaginary parts of its eigenvalues. The inverse of B 2 n is also determined. Related results obtained in previous articles are proven to be corollaries.

How to cite

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Wang, Chuanlong, and Yong, Xuerong. "Some properties complementary to Brualdi-Li matrices." Czechoslovak Mathematical Journal 65.1 (2015): 135-149. <http://eudml.org/doc/270048>.

@article{Wang2015,
abstract = {In this paper we derive new properties complementary to an $2n \times 2n$ Brualdi-Li tournament matrix $B_\{2n\}$. We show that $B_\{2n\}$ has exactly one positive real eigenvalue and one negative real eigenvalue and, as a by-product, reprove that every Brualdi-Li matrix has distinct eigenvalues. We then bound the partial sums of the real parts and the imaginary parts of its eigenvalues. The inverse of $B_\{2n\}$ is also determined. Related results obtained in previous articles are proven to be corollaries.},
author = {Wang, Chuanlong, Yong, Xuerong},
journal = {Czechoslovak Mathematical Journal},
keywords = {tournament matrix; Brualdi-Li matrix; eigenvalue; Perron value; tournament matrix; Brualdi-Li matrix; eigenvalue; Perron value},
language = {eng},
number = {1},
pages = {135-149},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some properties complementary to Brualdi-Li matrices},
url = {http://eudml.org/doc/270048},
volume = {65},
year = {2015},
}

TY - JOUR
AU - Wang, Chuanlong
AU - Yong, Xuerong
TI - Some properties complementary to Brualdi-Li matrices
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 1
SP - 135
EP - 149
AB - In this paper we derive new properties complementary to an $2n \times 2n$ Brualdi-Li tournament matrix $B_{2n}$. We show that $B_{2n}$ has exactly one positive real eigenvalue and one negative real eigenvalue and, as a by-product, reprove that every Brualdi-Li matrix has distinct eigenvalues. We then bound the partial sums of the real parts and the imaginary parts of its eigenvalues. The inverse of $B_{2n}$ is also determined. Related results obtained in previous articles are proven to be corollaries.
LA - eng
KW - tournament matrix; Brualdi-Li matrix; eigenvalue; Perron value; tournament matrix; Brualdi-Li matrix; eigenvalue; Perron value
UR - http://eudml.org/doc/270048
ER -

References

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