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All Journal JURNAL PENGABDIAN KEPADA MASYARAKAT BAREKENG: Jurnal Ilmu Matematika dan Terapan E-Amal: Jurnal Pengabdian Kepada Masyarakat
Santoso Budi Wiyono
Universitas Sebelas Maret
Agriculture, Biological Sciences & Forestry Arts Humanities Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Education Energy Engineering Health Professions Languange, Linguistic, Communication & Media Mathematics Mechanical Engineering Physics Social Sciences Transportation

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Journal : BAREKENG: Jurnal Ilmu Matematika dan Terapan

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MASALAH EIGEN DAN EIGENMODE MATRIKS ATAS ALJABAR MIN-PLUS Eka Widia Rahayu; Siswanto Siswanto; Santoso Budi Wiyono
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 15 No 4 (2021): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (514.39 KB) | DOI: 10.30598/barekengvol15iss4pp659-666

Abstract

Eigen problems and eigenmode are important components related to square matrices. In max-plus algebra, a square matrix can be represented in the form of a graph called a communication graph. The communication graph can be strongly connected graph and a not strongly connected graph. The representation matrix of a strongly connected graph is called an irreducible matrix, while the representation matrix of a graph that is not strongly connected is called a reduced matrix. The purpose of this research is set the steps to determine the eigenvalues and eigenvectors of the irreducible matrix over min-plus algebra and also eigenmode of the regular reduced matrix over min-plus algebra. Min-plus algebra has an ispmorphic structure with max-plus algebra. Therefore, eigen problems and eigenmode matrices over min-plus algebra can be determined based on the theory of eigenvalues, eigenvectors and eigenmode matrices over max-plus algebra. The results of this research obtained steps to determine the eigenvalues and eigenvectors of the irreducible matrix over min-plus algebra and eigenmode algorithm of the regular reduced matrix over min-plus algebra
Co-Authors Eka Widia Rahayu Siswanto Siswanto Siswanto Siswanto Siswanto Supriyadi Wibowo Supriyadi Wibowo Wibowo Sutrima Sutrima Sutrima Sutrima Sutrima Vika Yugi Kurniawan