SIMETRISASI BENTUK KANONIK JORDAN

  • Darlena Darlena Prodi Manajemen Informatika Akademi Manajemen Komputer dan Informatika (AMKI)
  • Ari Suparwanto Departemen Matematika FMIPA Universitas Gadjah Mada
DOI: https://doi.org/10.30598/barekengvol15iss1pp015-028
Keywords: Bentuk Kanonik Rasional, Bentuk Kanonik Jordan, Splitting Field

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

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References

J. B. Fraleigh, A First Course in Abstract Algebra, Seventh Edition, New York: Addison Wesley, 2003.

Kenneth Hoffman, Ray Kunze, Linear Algebra, New Jersey: Prentice-Hall, Inc, Engliwood Cliffts, 1971.

M. Radjabalipour, "The Rational Canonical Form Via The Splitting Field", Journal of Linear Algebra and Its Applications, pp. 2250-2255, July 2013.

M. Radjabalipour, "A Symmetrization of The Jordan Canonical Form", Journal of Linear Algebra and Its Applications, pp. 94-112, 2017.

S. H. Weintraub, Jordan Canonical Form, Theory and Practice, Washington: Morgan and Claypool Publisher, 2009.

Published
2021-03-01
How to Cite
[1]
D. Darlena and A. Suparwanto, “SIMETRISASI BENTUK KANONIK JORDAN”, BAREKENG: J. Math. & App., vol. 15, no. 1, pp. 015-028, Mar. 2021.
Issue
Vol 15 No 1 (2021): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Section
Articles

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