When does the inverse have the same sign pattern as the transpose?

Carolyn A. Eschenbach; Frank J. Hall; Deborah L. Harrell; Zhongshan Li

Czechoslovak Mathematical Journal (1999)

  • Volume: 49, Issue: 2, page 255-275
  • ISSN: 0011-4642

Abstract

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By a sign pattern (matrix) we mean an array whose entries are from the set { + , - , 0 } . The sign patterns A for which every real matrix with sign pattern A has the property that its inverse has sign pattern A T are characterized. Sign patterns A for which some real matrix with sign pattern A has that property are investigated. Some fundamental results as well as constructions concerning such sign pattern matrices are provided. The relation between these sign patterns and the sign patterns of orthogonal matrices is examined.

How to cite

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Eschenbach, Carolyn A., et al. "When does the inverse have the same sign pattern as the transpose?." Czechoslovak Mathematical Journal 49.2 (1999): 255-275. <http://eudml.org/doc/30483>.

@article{Eschenbach1999,
abstract = {By a sign pattern (matrix) we mean an array whose entries are from the set $\lbrace +,-,0\rbrace $. The sign patterns $A$ for which every real matrix with sign pattern $A$ has the property that its inverse has sign pattern $A^T$ are characterized. Sign patterns $A$ for which some real matrix with sign pattern $A$ has that property are investigated. Some fundamental results as well as constructions concerning such sign pattern matrices are provided. The relation between these sign patterns and the sign patterns of orthogonal matrices is examined.},
author = {Eschenbach, Carolyn A., Hall, Frank J., Harrell, Deborah L., Li, Zhongshan},
journal = {Czechoslovak Mathematical Journal},
keywords = {orthogonal matrices; sign pattern matrix; inverse},
language = {eng},
number = {2},
pages = {255-275},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {When does the inverse have the same sign pattern as the transpose?},
url = {http://eudml.org/doc/30483},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Eschenbach, Carolyn A.
AU - Hall, Frank J.
AU - Harrell, Deborah L.
AU - Li, Zhongshan
TI - When does the inverse have the same sign pattern as the transpose?
JO - Czechoslovak Mathematical Journal
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 49
IS - 2
SP - 255
EP - 275
AB - By a sign pattern (matrix) we mean an array whose entries are from the set $\lbrace +,-,0\rbrace $. The sign patterns $A$ for which every real matrix with sign pattern $A$ has the property that its inverse has sign pattern $A^T$ are characterized. Sign patterns $A$ for which some real matrix with sign pattern $A$ has that property are investigated. Some fundamental results as well as constructions concerning such sign pattern matrices are provided. The relation between these sign patterns and the sign patterns of orthogonal matrices is examined.
LA - eng
KW - orthogonal matrices; sign pattern matrix; inverse
UR - http://eudml.org/doc/30483
ER -

References

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  2. 10.1006/jctb.1994.1059, Journal of Combinatorial Theory (B) 62 (1994), 133–152. (1994) MR1290635DOI10.1006/jctb.1994.1059
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  4. Some sign patterns that allow a real Inverse-Pair B and B - 1 , Linear Algebra and its Applications 252 (1997), 299-321. (1997) MR1428639
  5. Proceedings: Theory of Graphs and Its Applications, Publishing House of Czechoslovakia Academy of Sciences, Prague, 1964. (1964) MR0172259
  6. Matrix Analysis, Cambridge, 1985. (1985) MR0832183
  7. Topics in Matrix Analysis, Cambridge, 1991. (1991) MR1091716
  8. On sign patterns of orthogonal matrices, Master’s Thesis, Tam Chiang Univ., 1984. (1984) 
  9. Sign patterns of Inverse-Positive matrices, Linear Algebra and its Applications 24 (1979), 75–83. (1979) MR0524826
  10. Sign-nonsingular matrices and even cycles in directed graphs, Linear Algebra and its Applications 75 (1986), 27–41. (1986) Zbl0589.05050MR0825397
  11. Sign patterns that allow orthogonality, Linear Algebra and its Applications 235 (1996), 1–13. (1996) MR1374247

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