New results about semi-positive matrices

Jonathan Dorsey; Tom Gannon; Charles R. Johnson; Morrison Turnansky

Czechoslovak Mathematical Journal (2016)

  • Volume: 66, Issue: 3, page 621-632
  • ISSN: 0011-4642

Abstract

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Our purpose is to present a number of new facts about the structure of semipositive matrices, involving patterns, spectra and Jordon form, sums and products, and matrix equivalence, etc. Techniques used to obtain the results may be of independent interest. Examples include: any matrix with at least two columns is a sum, and any matrix with at least two rows, a product, of semipositive matrices. Any spectrum of a real matrix with at least elements is the spectrum of a square semipositive matrix, and any real matrix, except for a negative scalar matrix, is similar to a semipositive matrix. M-matrices are generalized to the non-square case and sign patterns that require semipositivity are characterized.

How to cite

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Dorsey, Jonathan, et al. "New results about semi-positive matrices." Czechoslovak Mathematical Journal 66.3 (2016): 621-632. <http://eudml.org/doc/286836>.

@article{Dorsey2016,
abstract = {Our purpose is to present a number of new facts about the structure of semipositive matrices, involving patterns, spectra and Jordon form, sums and products, and matrix equivalence, etc. Techniques used to obtain the results may be of independent interest. Examples include: any matrix with at least two columns is a sum, and any matrix with at least two rows, a product, of semipositive matrices. Any spectrum of a real matrix with at least $2$ elements is the spectrum of a square semipositive matrix, and any real matrix, except for a negative scalar matrix, is similar to a semipositive matrix. M-matrices are generalized to the non-square case and sign patterns that require semipositivity are characterized.},
author = {Dorsey, Jonathan, Gannon, Tom, Johnson, Charles R., Turnansky, Morrison},
journal = {Czechoslovak Mathematical Journal},
keywords = {sign semipositivity; semipositive matrix; M-matrix; spectrum; equivalence},
language = {eng},
number = {3},
pages = {621-632},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {New results about semi-positive matrices},
url = {http://eudml.org/doc/286836},
volume = {66},
year = {2016},
}

TY - JOUR
AU - Dorsey, Jonathan
AU - Gannon, Tom
AU - Johnson, Charles R.
AU - Turnansky, Morrison
TI - New results about semi-positive matrices
JO - Czechoslovak Mathematical Journal
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 3
SP - 621
EP - 632
AB - Our purpose is to present a number of new facts about the structure of semipositive matrices, involving patterns, spectra and Jordon form, sums and products, and matrix equivalence, etc. Techniques used to obtain the results may be of independent interest. Examples include: any matrix with at least two columns is a sum, and any matrix with at least two rows, a product, of semipositive matrices. Any spectrum of a real matrix with at least $2$ elements is the spectrum of a square semipositive matrix, and any real matrix, except for a negative scalar matrix, is similar to a semipositive matrix. M-matrices are generalized to the non-square case and sign patterns that require semipositivity are characterized.
LA - eng
KW - sign semipositivity; semipositive matrix; M-matrix; spectrum; equivalence
UR - http://eudml.org/doc/286836
ER -

References

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