Studying the various properties of MIN and MAX matrices - elementary vs. more advanced methods
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 interpr...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2016-01-01
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| Series: | Special Matrices |
| Subjects: | |
| Online Access: | http://www.degruyter.com/view/j/spma.2016.4.issue-1/spma-2016-0010/spma-2016-0010.xml?format=INT |
| _version_ | 1830353316764188672 |
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| author | Mattila Mika Haukkanen Pentti |
| author_facet | Mattila Mika Haukkanen Pentti |
| author_sort | Mattila Mika |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-20T01:11:34Z |
| format | Article |
| id | doaj.art-9364a98937574b59a9d43aab143a812d |
| institution | Directory Open Access Journal |
| issn | 2300-7451 |
| language | English |
| last_indexed | 2024-12-20T01:11:34Z |
| publishDate | 2016-01-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Special Matrices |
| spelling | doaj.art-9364a98937574b59a9d43aab143a812d2022-12-21T19:58:40ZengDe GruyterSpecial Matrices2300-74512016-01-014110.1515/spma-2016-0010spma-2016-0010Studying the various properties of MIN and MAX matrices - elementary vs. more advanced methodsMattila Mika0Haukkanen Pentti1Department of Mathematics, Tampere University of Technology, FinlandSchool of Information Sciences, University of Tampere, FinlandLet 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.http://www.degruyter.com/view/j/spma.2016.4.issue-1/spma-2016-0010/spma-2016-0010.xml?format=INTMIN matrixMAX matrix meet matrix join matrix |
| spellingShingle | Mattila Mika Haukkanen Pentti Studying the various properties of MIN and MAX matrices - elementary vs. more advanced methods Special Matrices MIN matrix MAX matrix meet matrix join matrix |
| title | Studying the various properties of MIN and
MAX matrices - elementary vs. more advanced
methods |
| title_full | Studying the various properties of MIN and
MAX matrices - elementary vs. more advanced
methods |
| title_fullStr | Studying the various properties of MIN and
MAX matrices - elementary vs. more advanced
methods |
| title_full_unstemmed | Studying the various properties of MIN and
MAX matrices - elementary vs. more advanced
methods |
| title_short | Studying the various properties of MIN and
MAX matrices - elementary vs. more advanced
methods |
| title_sort | studying the various properties of min and max matrices elementary vs more advanced methods |
| topic | MIN matrix MAX matrix meet matrix join matrix |
| url | http://www.degruyter.com/view/j/spma.2016.4.issue-1/spma-2016-0010/spma-2016-0010.xml?format=INT |
| work_keys_str_mv | AT mattilamika studyingthevariouspropertiesofminandmaxmatriceselementaryvsmoreadvancedmethods AT haukkanenpentti studyingthevariouspropertiesofminandmaxmatriceselementaryvsmoreadvancedmethods |