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 |
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Canonical name | ConductorOfAVector |
Date of creation | 2013-03-22 14:05:19 |
Last modified on | 2013-03-22 14:05:19 |
Owner | CWoo (3771) |
Last modified by | CWoo (3771) |
Numerical id | 5 |
Author | CWoo (3771) |
Entry type | Definition |
Classification | msc 15A04 |
Synonym | T-conductor |
Synonym | conductor |
Synonym | annihilator |
Synonym | annihilator polynomial |
Synonym | conductor polynomial |