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ITS » Paper and Presentation » Matematika - S2
Posted by anisw@its.ac.id at 24/05/2016 09:11:01  •  1054 Views


EIGENVALUE EIGENVECTOR AND EIGENMODE CHARACTERIZATION OF IRREDUCIBLE AND REDUCIBLE MATRIX IN THE MAX-PLUS ALGEBRA

KARAKTERISASI NILAI EIGEN VEKTOR EIGEN DAN EIGENMODE DARI MATRIKS TAK TEREDUKSI DAN TEREDUKSI DALAM ALJABAR MAX-PLUS

Author :
MURSYIDAH, HIMMATUL ( 1213201001 )




ABSTRAK

Terdapat dua jenis graf dalam aljabar max-plus berdasarkan sifat keterhubungannya yaitu graf strongly connected dan graf tidak strongly connected. Matriks representasi dari graf strongly connected disebut matriks tak tereduksi sedangkan matriks representasi dari graf tidak strongly connected disebut matriks tereduksi. Berdasarkan hasil penelitian diperoleh bahwa matriks tak tereduksi memiliki nilai eigen tunggal berhingga. Vektor eigen yang bersesuaian dengan nilai eigen dari matriks tak tereduksi tidak tunggal dan memiliki nilai berhingga untuk setiap elemennya. Sedangkan eigenmode dari matriks tak tereduksi tidak tunggal dengan semua elemen berhingga untuk setiap komponen vektornya. Adapun matriks tereduksi belum tentu memiliki nilai eigen. Jika matriks tereduksi memiliki nilai eigen maka nilai eigen tersebut belum tentu tunggal dengan nilai berhingga. Selanjutnya vektor eigen yang bersesuaian dengan nilai eigen dari matriks tereduksi tidak tunggal dengan elemen vektor eigen paling sedikit memuat satu elemen berhingga. Sedangkan eigenmode dari matriks tereduksi reguler tidak tunggal dengan semua elemen berhingga untuk setiap komponen vektor dari eigenmode tersebut.


ABSTRACT

There are two types of graph in max-plus algebra based on the connectedness property they are strongly and not strongly connected graph. Matrix representation of a strongly connected graph is called irreducible matrix while matrix representation of not strongly connected graph is called reducible matrix. The results show that irreducible matrix has a unique and finite eigenvalue. Eigenvector corresponding to the eigenvalue of irreducible matrix is not unique and they have finite values for each element. While eigenmode of irreducible matrix is not unique with all finite elements for each vector component. Reducible matrix does not necessarily have eigenvalue. If reducible matrix has eigenvalue the eigenvalue is not necessarily unique with finite values. Furthermore eigenvector corresponding to the eigenvalue of reducible matrix is not unique that contains at least one finite element. While eigenmode of regular reducible matrix is not unique with all finite elements for each vector component.



Keywordsaljabar max-plus; eigenmode; matriks tak tereduksi; matriks tereduksi; nilai eigen; vektor eigen
 
Subject:  None
Contributor
  1. Dr. Subiono, M.S.
Date Create: 22/01/2015
Type: Text
Format: pdf
Language: Indonesian
Identifier: ITS-paper-12121160008981
Collection ID: 12121160008981
Call Number: RTMa 512.943 4 Mur k


Source
Paper and Presentations, Mathematics, RTMa 512.943 4 Mur k, 2015

Coverage
ITS Community

Rights
Copyright @2016 by ITS Library. This publication is protected by copyright and per obtained from the ITS Library prior to any prohibited reproduction, storage in a re transmission in any form or by any means, electronic, mechanical, photocopying, reco For information regarding permission(s), write to ITS Library




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  1.  ITS-paper-41591-1213201001-paperpdf.pdf - 382 KB
  2.  ITS-paper-41591-1213201001-presentationpdf.pdf - 2004 KB




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