Show that if a is greater than or equal to the degree of minimal polyn

[catsarebad]

Homework Statement

Show that if a is greater than or equal to the degree of minimal polynomial (say k), then L^a is a linear combination of 1v,L,…,Lk−1

If L is invertible, show the same for all a<0

Homework Equations

about minimal polynomial
http://en.wikipedia.org/wiki/Minimal_polynomial_(linear_algebra )

The Attempt at a Solution

i know a few things about minimal polynomial, i know what linear combination, invertible means but i have no clue how to start this problem.

i think the most confusing part i find is that i don't know how to deal with
L^a and the 1_v,L,...,L^k-1

 

[Ray Vickson]

Homework Statement

Show that if a is greater than or equal to the degree of minimal polynomial (say k), then L^a is a linear combination of 1v,L,…,Lk−1

If L is invertible, show the same for all a<0

Homework Equations

about minimal polynomial
http://en.wikipedia.org/wiki/Minimal_polynomial_(linear_algebra )

The Attempt at a Solution

i know a few things about minimal polynomial, i know what linear combination, invertible means but i have no clue how to start this problem.

i think the most confusing part i find is that i don't know how to deal with
L^a and the 1_v,L,...,L^k-1

Read my response to your other question about minimal polynomials.

 

[catsarebad]

delete this post.