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.
- Extremum Test
- Extrinsic Curvature
- Fabry Imbedding
- Face
- Facet
- Faceting
- Factor
- Factor Base
- Factor (Graph)
- Factor Group
- Factorial
- Factorial Moment
- Factorial Number
- Factorial Prime
- Factorial Sum
- Factoring
- Factorion
- Factorization
- Factor Level
- Factor Ring
- Factor Space
- Fagnano's Point
- Fagnano's Problem
- Fagnano's Theorem
- Fair Game