## Rational Canonical Form

There is an invertible matrix such that

where is the companion Matrix for any Monic Polynomial

with . The Polynomials are called the invariant factors'' of , and satisfy for , ..., 1 (Hartwig 1996).

References

Gantmacher, F. R. The Theory of Matrices, Vol. 1. New York: Chelsea, 1960.

Hartwig, R. E. Roth's Removal Rule and the Rational Canonical Form.'' Amer. Math. Monthly 103, 332-335, 1996.

Herstein, I. N. Topics in Algebra, 2nd ed. New York: Springer-Verlag, p. 162, 1975.

Hoffman, K. and Kunze, K. Linear Algebra, 3rd ed. Englewood Cliffs, NJ: Prentice-Hall, 1996.

Lancaster, P. and Tismenetsky, M. The Theory of Matrices, 2nd ed. New York: Academic Press, 1985.

Turnbull, H. W. and Aitken, A. C. An Introduction to the Theory of Canonical Matrices, 2nd impression. New York: Blackie and Sons, 1945.