A Hadamard product involving inverse-positive matrices

Gassó Maria T.; Torregrosa Juan R.; Abad Manuel

Special Matrices (2015)

  • Volume: 3, Issue: 1, page 193-199, electronic only
  • ISSN: 2300-7451

Abstract

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In this paperwe study the Hadamard product of inverse-positive matrices.We observe that this class of matrices is not closed under the Hadamard product, but we show that for a particular sign pattern of the inverse-positive matrices A and B, the Hadamard product A ◦ B−1 is again an inverse-positive matrix.

How to cite

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Gassó Maria T., Torregrosa Juan R., and Abad Manuel. "A Hadamard product involving inverse-positive matrices." Special Matrices 3.1 (2015): 193-199, electronic only. <http://eudml.org/doc/271769>.

@article{GassóMariaT2015,
abstract = {In this paperwe study the Hadamard product of inverse-positive matrices.We observe that this class of matrices is not closed under the Hadamard product, but we show that for a particular sign pattern of the inverse-positive matrices A and B, the Hadamard product A ◦ B−1 is again an inverse-positive matrix.},
author = {Gassó Maria T., Torregrosa Juan R., Abad Manuel},
journal = {Special Matrices},
keywords = {Hadamard product; inverse-positive matrices; sign pattern},
language = {eng},
number = {1},
pages = {193-199, electronic only},
title = {A Hadamard product involving inverse-positive matrices},
url = {http://eudml.org/doc/271769},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Gassó Maria T.
AU - Torregrosa Juan R.
AU - Abad Manuel
TI - A Hadamard product involving inverse-positive matrices
JO - Special Matrices
PY - 2015
VL - 3
IS - 1
SP - 193
EP - 199, electronic only
AB - In this paperwe study the Hadamard product of inverse-positive matrices.We observe that this class of matrices is not closed under the Hadamard product, but we show that for a particular sign pattern of the inverse-positive matrices A and B, the Hadamard product A ◦ B−1 is again an inverse-positive matrix.
LA - eng
KW - Hadamard product; inverse-positive matrices; sign pattern
UR - http://eudml.org/doc/271769
ER -

References

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  1. [1] S.M. Fallat, C.R. Johnson, Hadamard powers and totally positive matrices, Linear Algebra Appl., 423 (2007) 420-427.  
  2. [2] K. Fan, Inequalities for M-matrices, Nederl. Akad. Wetensch. Proc. Ser. A67 (1964) 602-610.  
  3. [3] C.R. Johnson, A Hadamard Product Involving M-matrices, Linear Multilinear Algebra, 4 (1977) 261-264. [Crossref] 
  4. [4] C.R. Johnson, R.L. Smith, Path Product matrices, Linear Multilinear Algebra, 46 (1999) 177-191.  
  5. [5] Y. Shangjun, C. Qian, On Oppenheim’s inequality, Numerical Mathematics, 14(2) (2005) 97-101.  
  6. [6] B.Y. Wang, X. Zhang, F. Zhang, On the Hadamard Product of Inverse M-matrices, Linear Algebra Appl., 305 (2000) 23-31.  

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