Consistency examination of linear inequality system

Henryk Brzeskwiniewicz; Krzysztof Kłaczyński

Consistency examination of linear inequality system

Henryk Brzeskwiniewicz; Krzysztof Kłaczyński

Mathematica Applicanda (1997)

Volume: 26, Issue: 40
ISSN: 1730-2668

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An investigation of the consistency of a linear inequality system is considered. It is proven that the system of linear inequalities Ax≥b is consistent if and only if for any generalized inverse A− of a matrix A the system of equations (I−AA−)v=−(I−AA−)b has a nonnegative solution for the vector v. Consistency of the above system does not depend on the choice of the matrix A−. The paper also presents methods for investigating the existence of nonnegative solutions of systems of linear equations.

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Henryk Brzeskwiniewicz, and Krzysztof Kłaczyński. "Consistency examination of linear inequality system." Mathematica Applicanda 26.40 (1997): null. <http://eudml.org/doc/293356>.

@article{HenrykBrzeskwiniewicz1997,
abstract = {An investigation of the consistency of a linear inequality system is considered. It is proven that the system of linear inequalities Ax≥b is consistent if and only if for any generalized inverse A− of a matrix A the system of equations (I−AA−)v=−(I−AA−)b has a nonnegative solution for the vector v. Consistency of the above system does not depend on the choice of the matrix A−. The paper also presents methods for investigating the existence of nonnegative solutions of systems of linear equations.},
author = {Henryk Brzeskwiniewicz, Krzysztof Kłaczyński},
journal = {Mathematica Applicanda},
keywords = {Linear inequalities},
language = {eng},
number = {40},
pages = {null},
title = {Consistency examination of linear inequality system},
url = {http://eudml.org/doc/293356},
volume = {26},
year = {1997},
}

TY - JOUR
AU - Henryk Brzeskwiniewicz
AU - Krzysztof Kłaczyński
TI - Consistency examination of linear inequality system
JO - Mathematica Applicanda
PY - 1997
VL - 26
IS - 40
SP - null
AB - An investigation of the consistency of a linear inequality system is considered. It is proven that the system of linear inequalities Ax≥b is consistent if and only if for any generalized inverse A− of a matrix A the system of equations (I−AA−)v=−(I−AA−)b has a nonnegative solution for the vector v. Consistency of the above system does not depend on the choice of the matrix A−. The paper also presents methods for investigating the existence of nonnegative solutions of systems of linear equations.
LA - eng
KW - Linear inequalities
UR - http://eudml.org/doc/293356
ER -

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