Article Per Year (5 Year)
p-Index From 2021 - 2026
0.659
P-Index
This Author published in this journals
All Journal Jurnal Matematika MATEMATIKA Jurnal Natur Indonesia Jurnal Sains Dasar Journal of the Indonesian Mathematical Society Jurnal Matematika & Sains JMPM: Jurnal Matematika dan Pendidikan Matematika BAREKENG: Jurnal Ilmu Matematika dan Terapan Majalah Ilmiah Matematika dan Statistika (MIMS)
ARI SUPARWANTO
Unknown Affiliation
Agriculture, Biological Sciences & Forestry Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Chemistry Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Education Energy Engineering Mathematics Mechanical Engineering Physics Transportation

Published : 14 Documents Claim Missing Document
Claim Missing Document
Check
Articles

Found 14 Documents
Search

 1   2 
Diagonalisasi matriks atas ring dengan metode pemfaktoran secara lengkap Nikita, Nikita; Suparwanto, Ari; Sutopo, Sutopo
Majalah Ilmiah Matematika dan Statistika Vol. 24 No. 2 (2024): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v24i2.35918

Abstract

Generally, discussion about diagonalization of matrices in linear algebra is a matrix over the field. This research presents the diagonalization of matrices over commutative rings. Previous studies have explained the diagonalization of the matrix over a commutative ring, but there are some shortcomings in it. Therefore, this paper will present a matrix diagonalization process that could overcome these shortcomings. This research proposes a method for diagonalization matrices where the characteristic polynomial splits completely over the image of a ring homomorphism. Furthermore, the diagonalization is done over ring localization, so that there are more commutative ring matrices which can be diagonalized in this way. Meanwhile, the sufficient condition for a matrix which can be diagonalized in this thesis is when the determinant of the matrix whose columns are the eigenvectors is regular. Furthermore, to show this diagonalization method applies in general, given a special matrix n × n which satisfies the sufficient condition. Keywords: Matrices, diagonalization, eigenvector, determinant, localizationMSC2020: 15A09, 15A18, 15A20,13B05,13B20
Representasi Nilai Eigen Matriks atas Aljabar Maks-Plus Tersimetri dengan ELCP Ariyanti, Gregoria; Suparwanto, Ari; Surodjo, Budi
JMPM: Jurnal Matematika dan Pendidikan Matematika Vol 5 No 2 (2020): September 2020 - February 2021
Publisher : Prodi Pendidikan Matematika Universitas Pesantren Tinggi Darul Ulum Jombang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26594/jmpm.v5i2.1942

Abstract

Aljabar maks-plus tersimetri merupakan perluasan dari aljabar maks-plus. Karena matriks atas aljabar maks-plus tersimetri dapat didefinisikan determinan maka persamaan karakteristiknya dapat diformulasikan sebagai sistem persamaan polinomial multivariabel aljabar maks-plus. Diperlukan suatu langkah menentukan nilai eigen dengan menggunakan alat yang disebut Masalah Linear Komplementer Diperluas (Extended Linear Complementarity Problem atau ELCP). Dalam tulisan ini, dipaparkan penggunaan ELCP dalam menentukan nilai eigen matriks atas aljabar maks-plus tersimetri. Penggunaan ELCP dilakukan dengan langkah-langkah yaitu mengubah persamaan karakteristik yang diperoleh dari suatu matriks ke bentuk sistem kesetimbangan linear. Selanjutnya, akar persamaan karakteristik yang diperoleh  merupakan penyelesaian dari sistem kesetimbangan linear yang merupakan nilai eigen dari matriks tersebut. Akibatnya, diperoleh representasi nilai eigen matriks atas aljabar maks-plus tersimetri dengan ELCP.
SIMETRISASI BENTUK KANONIK JORDAN Darlena, Darlena; Suparwanto, Ari
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 15 No 1 (2021): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (469.957 KB) | DOI: 10.30598/barekengvol15iss1pp015-028

Abstract

If the characteristic polynomial of a linear operator is completely factored in scalar field of then Jordan canonical form of can be converted to its rational canonical form of , and vice versa. If the characteristic polynomial of linear operator is not completely factored in the scalar field of ,then the rational canonical form of can still be obtained but not its Jordan canonical form matrix . In this case, the rational canonical form of can be converted to its Jordan canonical form by extending the scalar field of to Splitting Field of minimal polynomial of , thus forming the Jordan canonical form of over Splitting Field of . Conversely, converting the Jordan canonical form of over Splitting Field of to its rational canonical form uses symmetrization on the Jordan decomposition basis of so as to form a cyclic decomposition basis of which is then used to form the rational canonical matrix of
APPLICATION OF SYSTEM MAX-PLUS LINEAR EQUATIONS ON SERIAL MANUFACTURING MACHINE WITH STORAGE UNIT Maharani, Andika Ellena Saufika Hakim; Suparwanto, Ari
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 16 No 2 (2022): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (388.929 KB) | DOI: 10.30598/barekengvol16iss2pp525-530

Abstract

The set together with the operation maximum (max) denoted as and addition (+) denoted as is called max-plus algebra. Max-plus algebra may be used to apply algebraically a few programs of Discrete Event Systems (DES), certainly one of the examples in the production system. In this study, the application of max-plus algebra in a serial manufacturing machine with a storage unit is discussed. The results of this are the generalization system max-plus-linear equations on a production system that is, in addition, noted the max-plus-linear time-invariant system. From the max-plus-linear time-invariant system, it can be obtained the equation which is then used to determine the beginning time of a production system so the manufacturing machine work periodically. The eigenvector and eigenvalue of the matrix are then used to find the beginning time and the period time of the manufacturing machine. Furthermore, the time when the product leaves the manufacturing machine with the time while the raw material enters the manufacturing machine is given and vice versa are obtained from the max-plus-linear time-invariant system that is can be formed in the equation .
Co-Authors Andi Rudhito Budi Surodjo Darlena, Darlena Eka Susilowati F Susilo F. SUSILO Frans Susilo Gregoria Ariyanti M Andy Rudhito M. Andy Rudhito M. Andy Rudhito M. ANDY RUDHITO Maharani, Andika Ellena Saufika Hakim Marcellinus Andy Rudhito Maxrizal Nikita S Siswanto Sri Wahyuni Sri Wahyuni Sutopo Sutopo