conductor of a vector
Let be a field, a vector space, a linear transformation, and a -invariant subspace of . Let . The -conductor of in is the set containing all polynomials such that . It happens to be that this set is an ideal of the polynomial ring. We also use the term -conductor of in to refer to the generator of such ideal.
In the special case , the -conductor is called -annihilator of . Another way to define the -conductor of in is by saying that it is a monic polynomial of lowest degree such that . Of course this polynomial happens to be unique. So the -annihilator of is the monic polynomial of lowest degree such that .
|Title||conductor of a vector|
|Date of creation||2013-03-22 14:05:19|
|Last modified on||2013-03-22 14:05:19|
|Last modified by||CWoo (3771)|