• Support PF! Buy your school textbooks, materials and every day products Here!

Minimal Polynomial Question

  • Thread starter CoachZ
  • Start date
  • #1
26
0

Homework Statement



Let V be the vector space of n x n matrices over the field F. Fix [tex] A \in V[/tex]. Let T be the linear operator on V defined by T(B) = AB, for all [tex] B \in V[/tex].

a). Show that the minimal polynomial for T equals the minimal polynomial for A.
b) Find the matrix of T with respect the the standard basis of V. i.e. the basis [tex]\left\{E_{ij} \right| 1 \leq i,j \leq n [/tex]}, where [tex]E_{ij}[/tex] is the matrix having 1 in the (i,j)th entry and zeros everywhere else.

Homework Equations



...

The Attempt at a Solution



I know that the operator T is represented in some ordered basis by the matrix A, then T and A have the same minimal polynomial. The problem I'm running into is that I'm having a really hard time understanding abstract linear algebra, so this is all very very confusing to me and I'm not quite sure where to even start on this problem...
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,770
911
What is the definition of "minimal polynomial" for a linear operator?
 

Related Threads for: Minimal Polynomial Question

Replies
3
Views
998
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
2
Views
819
  • Last Post
Replies
3
Views
1K
Replies
6
Views
4K
  • Last Post
Replies
6
Views
1K
Replies
3
Views
3K
Top