Symmetric sign patterns with maximal inertias

In-Jae Kim; Charles Waters

Czechoslovak Mathematical Journal (2010)

  • Volume: 60, Issue: 1, page 101-104
  • ISSN: 0011-4642

Abstract

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The inertia of an n by n symmetric sign pattern is called maximal when it is not a proper subset of the inertia of another symmetric sign pattern of order n . In this note we classify all the maximal inertias for symmetric sign patterns of order n , and identify symmetric sign patterns with maximal inertias by using a rank-one perturbation.

How to cite

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Kim, In-Jae, and Waters, Charles. "Symmetric sign patterns with maximal inertias." Czechoslovak Mathematical Journal 60.1 (2010): 101-104. <http://eudml.org/doc/37992>.

@article{Kim2010,
abstract = {The inertia of an $n$ by $n$ symmetric sign pattern is called maximal when it is not a proper subset of the inertia of another symmetric sign pattern of order $n$. In this note we classify all the maximal inertias for symmetric sign patterns of order $n$, and identify symmetric sign patterns with maximal inertias by using a rank-one perturbation.},
author = {Kim, In-Jae, Waters, Charles},
journal = {Czechoslovak Mathematical Journal},
keywords = {eigenvalue; inertia; maximal inertia; rank-one perturbation; symmetric sign pattern; eigenvalue; inertia; maximal inertia; rank-one perturbation; symmetric sign pattern},
language = {eng},
number = {1},
pages = {101-104},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Symmetric sign patterns with maximal inertias},
url = {http://eudml.org/doc/37992},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Kim, In-Jae
AU - Waters, Charles
TI - Symmetric sign patterns with maximal inertias
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 1
SP - 101
EP - 104
AB - The inertia of an $n$ by $n$ symmetric sign pattern is called maximal when it is not a proper subset of the inertia of another symmetric sign pattern of order $n$. In this note we classify all the maximal inertias for symmetric sign patterns of order $n$, and identify symmetric sign patterns with maximal inertias by using a rank-one perturbation.
LA - eng
KW - eigenvalue; inertia; maximal inertia; rank-one perturbation; symmetric sign pattern; eigenvalue; inertia; maximal inertia; rank-one perturbation; symmetric sign pattern
UR - http://eudml.org/doc/37992
ER -

References

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  1. Cavers, M. S., Meulen, K. N. Vander, Spectrally and inertially arbitrary sign patterns, Linear Algebra Appl. 394 (2005), 53-72. (2005) MR2100576
  2. Fonseca, C. M. da, 10.1007/s10587-006-0062-0, Czechoslovak Math. J. 56 (2006), 875-883. (2006) Zbl1164.15318MR2261659DOI10.1007/s10587-006-0062-0
  3. Gao, Y., Shao, Y., 10.1023/B:CMAJ.0000024531.10708.9f, Czechoslovak Math. J. 53 (2003), 925-934. (2003) Zbl1080.15501MR2018840DOI10.1023/B:CMAJ.0000024531.10708.9f
  4. Horn, R. A., Johnson, C. R., Matrix Analysis, Cambridge Univeristy Press Cambridge (1985). (1985) Zbl0576.15001MR0832183
  5. Hall, F. J., Li, Z., Inertia sets of symmetric sign pattern matrices, Numer. Math., J. Chin. Univ. (English Ser.) 10 (2001), 226-240. (2001) Zbl0997.15010MR1884971
  6. Hall, F. J., Li, Z., Wang, Di, Symmetric sign pattern matrices that require unique inertia, Linear Algebra Appl. 338 (2001), 153-169. (2001) Zbl0994.15028MR1861120
  7. Hall, F. J., Li, Z., Wang, Di, Symmetric sign pattern matrices that require unique inertia, Linear Algebra Appl. 338 (2001), 153-169. (2001) Zbl0994.15028MR1861120

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