± sign pattern matrices that allow orthogonality

Yan Ling Shao; Liang Sun; Yubin Gao

Czechoslovak Mathematical Journal (2006)

  • Volume: 56, Issue: 3, page 969-979
  • ISSN: 0011-4642

Abstract

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A sign pattern A is a ± sign pattern if A has no zero entries. A allows orthogonality if there exists a real orthogonal matrix B whose sign pattern equals A . Some sufficient conditions are given for a sign pattern matrix to allow orthogonality, and a complete characterization is given for ± sign patterns with n - 1 ≤ N - ( A ) ≤ n + 1 to allow orthogonality.

How to cite

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Shao, Yan Ling, Sun, Liang, and Gao, Yubin. "$\pm $ sign pattern matrices that allow orthogonality." Czechoslovak Mathematical Journal 56.3 (2006): 969-979. <http://eudml.org/doc/31083>.

@article{Shao2006,
abstract = {A sign pattern $A$ is a $\pm $ sign pattern if $A$ has no zero entries. $A$ allows orthogonality if there exists a real orthogonal matrix $B$ whose sign pattern equals $A$. Some sufficient conditions are given for a sign pattern matrix to allow orthogonality, and a complete characterization is given for $\pm $ sign patterns with $n-1 \le N_-(A) \le n+1$ to allow orthogonality.},
author = {Shao, Yan Ling, Sun, Liang, Gao, Yubin},
journal = {Czechoslovak Mathematical Journal},
keywords = {sign pattern; orthogonality; orthogonal matrix; sign pattern; orthogonality; orthogonal matrix},
language = {eng},
number = {3},
pages = {969-979},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {$\pm $ sign pattern matrices that allow orthogonality},
url = {http://eudml.org/doc/31083},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Shao, Yan Ling
AU - Sun, Liang
AU - Gao, Yubin
TI - $\pm $ sign pattern matrices that allow orthogonality
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 3
SP - 969
EP - 979
AB - A sign pattern $A$ is a $\pm $ sign pattern if $A$ has no zero entries. $A$ allows orthogonality if there exists a real orthogonal matrix $B$ whose sign pattern equals $A$. Some sufficient conditions are given for a sign pattern matrix to allow orthogonality, and a complete characterization is given for $\pm $ sign patterns with $n-1 \le N_-(A) \le n+1$ to allow orthogonality.
LA - eng
KW - sign pattern; orthogonality; orthogonal matrix; sign pattern; orthogonality; orthogonal matrix
UR - http://eudml.org/doc/31083
ER -

References

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  1. Combinatorial orthogonality, In: Combinatorial and Graph-Theoretical Problems in Linear Algebra, R. A.  Brualdi, S.  Friedland, and V.  Klee (eds.), Springer-Verlag, Berlin, 1993, pp. 207–218. (1993) MR1240965
  2. 10.1006/jcta.1998.2898, Journal of Combinatorial Theory, Series A 85 (1999), 29–40. (1999) MR1659464DOI10.1006/jcta.1998.2898
  3. Sign pattern matrices that allow orthogonality, Linear Algebra Appl. 235 (1996), 1–16. (1996) Zbl0852.15018MR1374247
  4. The possible numbers of zeros in an orthogonal matrix, Electron.  J. Linear Algebra 5 (1999), 19–23. (1999) MR1659324
  5. 10.1023/A:1022496101277, Czechoslovak Math.  J. 124 (1999), 255–275. (1999) MR1692477DOI10.1023/A:1022496101277
  6. Matrix Analysis, Cambridge University Press, Cambridge, 1985. (1985) MR0832183

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