SIMETRISASI BENTUK KANONIK JORDAN

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...

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Main Authors: Darlena Darlena, Ari Suparwanto
Format: Article
Language:English
Published: Universitas Pattimura 2021-03-01
Series:Barekeng
Subjects:
Online Access:https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/2297
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author Darlena Darlena
Ari Suparwanto
author_facet Darlena Darlena
Ari Suparwanto
author_sort Darlena Darlena
collection DOAJ
description 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
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institution Kabale University
issn 1978-7227
2615-3017
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publishDate 2021-03-01
publisher Universitas Pattimura
record_format Article
series Barekeng
spelling doaj-art-11a1af3b401b429baec01fdfd8e625c22025-08-20T03:37:37ZengUniversitas PattimuraBarekeng1978-72272615-30172021-03-0115101502810.30598/barekengvol15iss1pp015-0282297SIMETRISASI BENTUK KANONIK JORDANDarlena Darlena0Ari Suparwanto1Prodi Manajemen Informatika Akademi Manajemen Komputer dan Informatika (AMKI)Departemen Matematika FMIPA Universitas Gadjah MadaIf 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 ofhttps://ojs3.unpatti.ac.id/index.php/barekeng/article/view/2297bentuk kanonik rasionalbentuk kanonik jordansplitting field
spellingShingle Darlena Darlena
Ari Suparwanto
SIMETRISASI BENTUK KANONIK JORDAN
Barekeng
bentuk kanonik rasional
bentuk kanonik jordan
splitting field
title SIMETRISASI BENTUK KANONIK JORDAN
title_full SIMETRISASI BENTUK KANONIK JORDAN
title_fullStr SIMETRISASI BENTUK KANONIK JORDAN
title_full_unstemmed SIMETRISASI BENTUK KANONIK JORDAN
title_short SIMETRISASI BENTUK KANONIK JORDAN
title_sort simetrisasi bentuk kanonik jordan
topic bentuk kanonik rasional
bentuk kanonik jordan
splitting field
url https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/2297
work_keys_str_mv AT darlenadarlena simetrisasibentukkanonikjordan
AT arisuparwanto simetrisasibentukkanonikjordan