A Minimality of the Rational Canonical Form

Heguo Liu; Honglian Zhang

doi:10.4236/alamt.2019.94006

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A Minimality of the Rational Canonical Form

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DOI: 10.4236/alamt.2019.94006 62 Downloads 111 Views

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Heguo Liu¹, Honglian Zhang²

Affiliation(s)

¹School of Mathematics and Statistics, Hubei University, Wuhan, China.
²Department of Mathematics, Shanghai University, Shanghai, China.

ABSTRACT

The rational canonical form theorem is very essential basic result of matrix theory, which has been proved by different methods in the literature. In this note, we provide an effcient direct proof, from which the minimality for the decomposition of the rational canonical form can be found.

KEYWORDS

Minimal Polynomial, Rational Canonical Form, Cyclic Subspace

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

Cite this paper

Liu, H. and Zhang, H. (2019) A Minimality of the Rational Canonical Form. Advances in Linear Algebra & Matrix Theory, 9, 83-88. doi: 10.4236/alamt.2019.94006.

References

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[4]	Hartwig, R.E. (1996) Roth's Removal Rule and the Rational Canonical Form. The American Mathematical Monthly, 103, 332- 335. https://doi.org/10.1080/00029890.1996.12004746