Previous |  Up |  Next


sign pattern; orthogonality; orthogonal matrix
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.
[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. MR 1240965
[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. DOI 10.1006/jcta.1998.2898 | MR 1659464
[3] C.  Waters: Sign pattern matrices that allow orthogonality. Linear Algebra Appl. 235 (1996), 1–16. MR 1374247 | 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. MR 1659324
[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. DOI 10.1023/A:1022496101277 | MR 1692477
[6] R. A.  Horn, C. R.  Johnson: Matrix Analysis. Cambridge University Press, Cambridge, 1985. MR 0832183
Partner of
EuDML logo