On complex power nonnegative matrices

Francesco Tudisco; Valerio Cardinali; Carmine Di Fiore

doi:10.1016/j.laa.2014.12.021

On complex power nonnegative matrices

Francesco Tudisco, Valerio Cardinali, Carmine Di Fiore

Mathematics And Statistics

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

Power nonnegative matrices are defined as complex matrices having at least one nonnegative integer power. We exploit the possibility of deriving a Perron–Frobenius-like theory for these matrices, obtaining three main results and drawing several consequences. We study, in particular, the relationships with the set of matrices having eventually nonnegative powers, the inverse of M-type matrices and the set of matrices whose columns (rows) sum up to one.

Original language	English
Pages (from-to)	449-468
Number of pages	20
Journal	Linear Algebra and its Applications
Volume	471
DOIs	https://doi.org/10.1016/j.laa.2014.12.021
Publication status	Published - 15 Apr 2015

Keywords

nonnegative matrices
eventually nonnegative matrices
power nonnegative matrices
stochastic matrices
Perron–Frobenius theory

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10.1016/j.laa.2014.12.021

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title = "On complex power nonnegative matrices",

abstract = "Power nonnegative matrices are defined as complex matrices having at least one nonnegative integer power. We exploit the possibility of deriving a Perron–Frobenius-like theory for these matrices, obtaining three main results and drawing several consequences. We study, in particular, the relationships with the set of matrices having eventually nonnegative powers, the inverse of M-type matrices and the set of matrices whose columns (rows) sum up to one.",

keywords = "nonnegative matrices, eventually nonnegative matrices, power nonnegative matrices, stochastic matrices, Perron–Frobenius theory",

author = "Francesco Tudisco and Valerio Cardinali and {Di Fiore}, Carmine",

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journal = "Linear Algebra and its Applications",

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T1 - On complex power nonnegative matrices

AU - Tudisco, Francesco

AU - Cardinali, Valerio

AU - Di Fiore, Carmine

PY - 2015/4/15

Y1 - 2015/4/15

N2 - Power nonnegative matrices are defined as complex matrices having at least one nonnegative integer power. We exploit the possibility of deriving a Perron–Frobenius-like theory for these matrices, obtaining three main results and drawing several consequences. We study, in particular, the relationships with the set of matrices having eventually nonnegative powers, the inverse of M-type matrices and the set of matrices whose columns (rows) sum up to one.

AB - Power nonnegative matrices are defined as complex matrices having at least one nonnegative integer power. We exploit the possibility of deriving a Perron–Frobenius-like theory for these matrices, obtaining three main results and drawing several consequences. We study, in particular, the relationships with the set of matrices having eventually nonnegative powers, the inverse of M-type matrices and the set of matrices whose columns (rows) sum up to one.

KW - nonnegative matrices

KW - eventually nonnegative matrices

KW - power nonnegative matrices

KW - stochastic matrices

KW - Perron–Frobenius theory

U2 - 10.1016/j.laa.2014.12.021

DO - 10.1016/j.laa.2014.12.021

M3 - Article

SN - 0024-3795

VL - 471

SP - 449

EP - 468

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

ER -

On complex power nonnegative matrices

Abstract

Keywords

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