×

\(\pm \) sign pattern matrices that allow orthogonality. (English) Zbl 1164.15327

Summary: 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 \(n-1 \leq N_-(A) \leq n+1\) to allow orthogonality.

MSC:

15B36 Matrices of integers
PDF BibTeX XML Cite
Full Text: DOI EuDML

References:

[1] L. B. Beasley, R. A. Brualdi, and B. L. Shader: 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. · Zbl 0789.15027
[2] G.-S. Cheon, B. L. Shader: How sparse can a matrix with orthogonal rows be? Journal of Combinatorial Theory, Series A 85 (1999), 29–40. · Zbl 0917.05014
[3] C. Waters: Sign pattern matrices that allow orthogonality. Linear Algebra Appl. 235 (1996), 1–16. · Zbl 0852.15018
[4] G.-S. Cheon, C. R. Johnson, S.-G. Lee, and E. J. Pribble: The possible numbers of zeros in an orthogonal matrix. Electron. J. Linear Algebra 5 (1999), 19–23. · Zbl 0918.15007
[5] C. A. Eschenbach, F. J. Hall, D. L. Harrell, and Z. Li: When does the inverse have the same pattern as the transpose? Czechoslovak Math. J. 124 (1999), 255–275. · Zbl 0954.15013
[6] R. A. Horn, C. R. Johnson: Matrix Analysis. Cambridge University Press, Cambridge, 1985. · Zbl 0576.15001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.