# $\pm $ 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

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topShao, 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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- 10.1006/jcta.1998.2898, Journal of Combinatorial Theory, Series A 85 (1999), 29–40. (1999) MR1659464DOI10.1006/jcta.1998.2898
- Sign pattern matrices that allow orthogonality, Linear Algebra Appl. 235 (1996), 1–16. (1996) Zbl0852.15018MR1374247
- The possible numbers of zeros in an orthogonal matrix, Electron. J. Linear Algebra 5 (1999), 19–23. (1999) MR1659324
- 10.1023/A:1022496101277, Czechoslovak Math. J. 124 (1999), 255–275. (1999) MR1692477DOI10.1023/A:1022496101277
- Matrix Analysis, Cambridge University Press, Cambridge, 1985. (1985) MR0832183

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