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Matriks atas aljabar max-plus

Anisianti, Desi Ayu (2013) Matriks atas aljabar max-plus. Undergraduate thesis, Universitas Islam Negeri Maulana Malik Ibrahim.

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Abstract

INDONESIA:

Aljabar max-plus (...) merupakan salah satu struktur aljabar yang semi-ring. Notasi ... menyatakan himpunan semua matriks berukuran nxn dengan entri-entrinya elemen R, dimana R merupakan himpunan bilangan real. Operasi ⊕ menyatakan maksimal dan operasi ⊗ menyatakan penjumlahan, yang didefinisikan sebagai berikut: ... merupakan semi-ring dengan matriks netral ... yang entri-entrinya yaitu ... dan matriks identitas ..., sehingga untuk ... berlaku sifat-sifat:
i.... membentuk semi-grup komutatif idempoten dengan matriks netral (ε), karena memiliki sifat asosiatif, komutatif dan terdapat matriks (ε).
ii. ... membentuk semi-grup, karena memiliki sifat asosiatif dan terdapat matriks identitas (E), serta memiliki matriks netral (ε) yang bersifat menyerap terhadap operasi....
iii. ... membentuk semi-ring idempoten, karena berdasarkan i dan ii operasi bersifat idempoten dan operasi ... bersifat distributif terhadap operasi ....

Maka disarankan kepada peneliti selanjutnya untuk membahas tentang aljabar max-plus pada matrik berordo mxn, aljabar max-plus pada fungsi skalar, pada masalah nilai eigen dan vektor eigen, aljabar max-plus pada grap dan aljabar max-plus dalam bentuk pemrograman agar lebih mudah menyelesaikannya.

ENGLISH:

An max-plus algebra (...) is one of the algebraic structure of a semi-ring. Notation ... states the set of all matrix of size n×n with entries element of R where R is the set of real numbers. Operation ⊕ states maximum and operation ⊗ states addition, which is defined as follows: ... is a semi-ring with neutral matrix (...) whose entries are ... and the identity matrix is ..., so that for ... the properties:
i. ... form a commutative idempotent semi-group with neutral matrix (ε), as has the nature of associative, commutative and there is a matrix of (ε).
ii. ... form a semi-group, because the properties are associative and the identity matrix (E), and has a neutral matrix (ε) which is absorbing the operations ....
iii. ... form a idempotent semi-ring, because based on i and ii are idempotent operations and is distributive operation on operation ....

Then suggested to the next researchers to discuss max-plus algebra on matrix order mxn. Max-plus algebra on scalar function, the problem eigen values and eigen vectors, max-plus algebra on graph, and max-plus algebra in the form of programming for easy finish.

Item Type: Thesis (Undergraduate)
Supervisor: Alisah, Evawati and Rozi, Fachrur
Contributors:
ContributionNameEmail
UNSPECIFIEDAlisah, EvawatiUNSPECIFIED
UNSPECIFIEDRozi, FachrurUNSPECIFIED
Keywords: Semi-grup; Semi-ring; Aljabar Max-plus; Semi-group; Semi-ring; Max-plus Algebra
Subjects: 01 MATHEMATICAL SCIENCES > 0101 Pure Mathematics > 010108 Operator Algebras and Functional Analysis
Departement: Fakultas Sains dan Teknologi > Jurusan Matematika
Depositing User: Luluk Handayani
Date Deposited: 12 Jun 2017 10:38
Last Modified: 12 Jun 2017 10:38
URI: http://etheses.uin-malang.ac.id/id/eprint/6868

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