Studying the various properties of MIN and MAX matrices - elementary vs. more advanced methods

Mika Mattila; Pentti Haukkanen

Special Matrices (2016)

  • Volume: 4, Issue: 1, page 101-109
  • ISSN: 2300-7451

Abstract

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Let T = {z1, z2, . . . , zn} be a finite multiset of real numbers, where z1 ≤ z2 ≤ · · · ≤ zn. The purpose of this article is to study the different properties of MIN and MAX matrices of the set T with min(zi , zj) and max(zi , zj) as their ij entries, respectively.We are going to do this by interpreting these matrices as so-called meet and join matrices and by applying some known results for meet and join matrices. Once the theorems are found with the aid of advanced methods, we also consider whether it would be possible to prove these same results by using elementary matrix methods only. In many cases the answer is positive.

How to cite

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Mika Mattila, and Pentti Haukkanen. "Studying the various properties of MIN and MAX matrices - elementary vs. more advanced methods." Special Matrices 4.1 (2016): 101-109. <http://eudml.org/doc/276414>.

@article{MikaMattila2016,
abstract = {Let T = \{z1, z2, . . . , zn\} be a finite multiset of real numbers, where z1 ≤ z2 ≤ · · · ≤ zn. The purpose of this article is to study the different properties of MIN and MAX matrices of the set T with min(zi , zj) and max(zi , zj) as their ij entries, respectively.We are going to do this by interpreting these matrices as so-called meet and join matrices and by applying some known results for meet and join matrices. Once the theorems are found with the aid of advanced methods, we also consider whether it would be possible to prove these same results by using elementary matrix methods only. In many cases the answer is positive.},
author = {Mika Mattila, Pentti Haukkanen},
journal = {Special Matrices},
keywords = {MIN matrix; MAX matrix; meet matrix; join matrix},
language = {eng},
number = {1},
pages = {101-109},
title = {Studying the various properties of MIN and MAX matrices - elementary vs. more advanced methods},
url = {http://eudml.org/doc/276414},
volume = {4},
year = {2016},
}

TY - JOUR
AU - Mika Mattila
AU - Pentti Haukkanen
TI - Studying the various properties of MIN and MAX matrices - elementary vs. more advanced methods
JO - Special Matrices
PY - 2016
VL - 4
IS - 1
SP - 101
EP - 109
AB - Let T = {z1, z2, . . . , zn} be a finite multiset of real numbers, where z1 ≤ z2 ≤ · · · ≤ zn. The purpose of this article is to study the different properties of MIN and MAX matrices of the set T with min(zi , zj) and max(zi , zj) as their ij entries, respectively.We are going to do this by interpreting these matrices as so-called meet and join matrices and by applying some known results for meet and join matrices. Once the theorems are found with the aid of advanced methods, we also consider whether it would be possible to prove these same results by using elementary matrix methods only. In many cases the answer is positive.
LA - eng
KW - MIN matrix; MAX matrix; meet matrix; join matrix
UR - http://eudml.org/doc/276414
ER -

References

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