theorem about cyclic subspaces

Let k be field, V a vector spaceMathworldPlanetmath over k, dimV=n, and T:VV a linear operatorMathworldPlanetmath. Let W be a subspacePlanetmathPlanetmathPlanetmath of V. And let v1,,vrV such that W=Z(v1,T)Z(vr,T) (see the cyclic subspace definition), and (mvi,mvj)=1 if ij, where mv denotes the minimal polynomial of v (or in other words, its annihilator polynomial). Then, Z(v1++vr,T)=Z(v1,T)Z(vr,T), and mv1++vr=mv1mvr.

Title theorem about cyclic subspaces
Canonical name TheoremAboutCyclicSubspaces
Date of creation 2013-03-22 14:15:16
Last modified on 2013-03-22 14:15:16
Owner Mathprof (13753)
Last modified by Mathprof (13753)
Numerical id 12
Author Mathprof (13753)
Entry type Theorem
Classification msc 15A04