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

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Studying the various properties of MIN and MAX matrices - elementary vs. more advanced methods. / Mattila, Mika; Haukkanen, Pentti.

julkaisussa: Special Matrices, Vuosikerta 4, Nro 1, 01.2016, s. 101-109.

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Mattila, Mika ; Haukkanen, Pentti. / Studying the various properties of MIN and MAX matrices - elementary vs. more advanced methods. Julkaisussa: Special Matrices. 2016 ; Vuosikerta 4, Nro 1. Sivut 101-109.

Bibtex - Lataa

@article{285e921a441e407cb78db6542d1036de,
title = "Studying the various properties of MIN and MAX matrices - elementary vs. more advanced methods",
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.",
keywords = "MIN matrix, MAX matrix, meet matrix, join matrix",
author = "Mika Mattila and Pentti Haukkanen",
year = "2016",
month = "1",
doi = "10.1515/spma-2016-0010",
language = "English",
volume = "4",
pages = "101--109",
journal = "Special Matrices",
issn = "2300-7451",
publisher = "De Gruyter Open Ltd.",
number = "1",

}

RIS (suitable for import to EndNote) - Lataa

TY - JOUR

T1 - Studying the various properties of MIN and MAX matrices - elementary vs. more advanced methods

AU - Mattila, Mika

AU - Haukkanen, Pentti

PY - 2016/1

Y1 - 2016/1

N2 - 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.

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.

KW - MIN matrix

KW - MAX matrix

KW - meet matrix

KW - join matrix

U2 - 10.1515/spma-2016-0010

DO - 10.1515/spma-2016-0010

M3 - Article

VL - 4

SP - 101

EP - 109

JO - Special Matrices

JF - Special Matrices

SN - 2300-7451

IS - 1

ER -