# On a nonnegative irreducible matrix that is similar to a positive matrix

Open Mathematics (2012)

• Volume: 10, Issue: 1, page 303-311
• ISSN: 2391-5455

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## Abstract

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Let A be an n×n irreducible nonnegative (elementwise) matrix. Borobia and Moro raised the following question: Suppose that every diagonal of A contains a positive entry. Is A similar to a positive matrix? We give an affirmative answer in the case n = 4.

## How to cite

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Raphael Loewy. "On a nonnegative irreducible matrix that is similar to a positive matrix." Open Mathematics 10.1 (2012): 303-311. <http://eudml.org/doc/269664>.

@article{RaphaelLoewy2012,
abstract = {Let A be an n×n irreducible nonnegative (elementwise) matrix. Borobia and Moro raised the following question: Suppose that every diagonal of A contains a positive entry. Is A similar to a positive matrix? We give an affirmative answer in the case n = 4.},
author = {Raphael Loewy},
journal = {Open Mathematics},
keywords = {Nonnegative matrix; Irreducible matrix; Diagonal of a matrix; nonnegative matrix; irreducible matrix; diagonal of a matrix; similarity; positive matrices},
language = {eng},
number = {1},
pages = {303-311},
title = {On a nonnegative irreducible matrix that is similar to a positive matrix},
url = {http://eudml.org/doc/269664},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Raphael Loewy
TI - On a nonnegative irreducible matrix that is similar to a positive matrix
JO - Open Mathematics
PY - 2012
VL - 10
IS - 1
SP - 303
EP - 311
AB - Let A be an n×n irreducible nonnegative (elementwise) matrix. Borobia and Moro raised the following question: Suppose that every diagonal of A contains a positive entry. Is A similar to a positive matrix? We give an affirmative answer in the case n = 4.
LA - eng
KW - Nonnegative matrix; Irreducible matrix; Diagonal of a matrix; nonnegative matrix; irreducible matrix; diagonal of a matrix; similarity; positive matrices
UR - http://eudml.org/doc/269664
ER -

## References

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1. [1] Borobia A., Moro J., On nonnegative matrices similar to positive matrices, Linear Algebra Appl., 1997, 266, 365–379 http://dx.doi.org/10.1016/S0024-3795(97)00362-5 Zbl0887.15019
2. [2] Brualdi R.A., Ryser H.J., Combinatorial Matrix Theory, Encyclopedia Math. Appl., 39, Cambridge University Press, Cambridge, 1991
3. [3] Laffey T.J., Extreme nonnegative matrices, Linear Algebra Appl., 1998, 275–276, 349–357 http://dx.doi.org/10.1016/S0024-3795(97)10059-3
4. [4] Laffey T.J., Loewy R., Šmigoc H., Nonnegative matrices that are similar to positive matrices, SIAM J. Matrix Anal. Appl., 2009, 31(2), 629–649 http://dx.doi.org/10.1137/070692807 Zbl1190.15036

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