# 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

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topMaria 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

top- [1] S.M. Fallat, C.R. Johnson, Hadamard powers and totally positive matrices, Linear Algebra Appl., 423 (2007) 420-427. Zbl1123.15014
- [2] K. Fan, Inequalities for M-matrices, Nederl. Akad. Wetensch. Proc. Ser. A67 (1964) 602-610.
- [3] C.R. Johnson, A Hadamard Product Involving M-matrices, Linear Multilinear Algebra, 4 (1977) 261-264. [Crossref]
- [4] C.R. Johnson, R.L. Smith, Path Product matrices, Linear Multilinear Algebra, 46 (1999) 177-191. Zbl0976.15016
- [5] Y. Shangjun, C. Qian, On Oppenheim’s inequality, Numerical Mathematics, 14(2) (2005) 97-101. Zbl1082.15032
- [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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