A Hadamard product involving inverse-positive matrices

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

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

@article{MariaT2015,
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 = {Maria T. Gassó, Juan R. Torregrosa, Manuel F. Abad},
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 - Maria T. Gassó
AU - Juan R. Torregrosa
AU - Manuel F. Abad
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. Zbl1123.15014
  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. Zbl0976.15016
  5. [5] Y. Shangjun, C. Qian, On Oppenheim’s inequality, Numerical Mathematics, 14(2) (2005) 97-101. Zbl1082.15032
  6. [6] B.Y. Wang, X. Zhang, F. Zhang, On the Hadamard Product of Inverse M-matrices, Linear Algebra Appl., 305 (2000) 23-31. Zbl0948.15004

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