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.
References
[1]
Halmos, P. (1974) Finite-Dimensional Vector Spaces. Springer-
Verlag, New York. https://doi.org/10.1007/978-1-4612-6387-6
[2]
Horn, R.A. and Johnson, C.R. (1985) Matrix Analysis. Cam-
bridge University Press, Cambridge.
[3]
Jacobson, N. (1953) Lectures in Abstract Algebras II Linear Al-
gebra. Springer-Verlag, New York.
https://doi.org/10.1007/978-1-4684-7053-6
[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
