cyclic vector theorem

Let K be a field, V a K-vector spaceMathworldPlanetmath of dimensionPlanetmathPlanetmath n, and f:VV a linear transformation. Then f has a cyclic vector if and only if every linear transformation g:VV which commutes with f is a polynomialPlanetmathPlanetmath of K[X] evaluated in f.

Title cyclic vector theorem
Canonical name CyclicVectorTheorem
Date of creation 2013-03-22 14:14:16
Last modified on 2013-03-22 14:14:16
Owner gumau (3545)
Last modified by gumau (3545)
Numerical id 5
Author gumau (3545)
Entry type Theorem
Classification msc 15A04
Related topic CyclicSubspace