Jordan Form of Linear Transformation Matrix: R_1[x]

[talolard]

Homework Statement

The question si to find the jordan form of the following, I think it is diagnizable and am wondering if i am misunderstanding something or if diagnizable is a subccase of jordan form:
Anyway
Given the vector space $$R_1[x]$$ i.e. the space of linear functions (a+bx) find the jordan form of the follwoing matrix
$$T(a+bx)=2a+b+bx$$
I thinbk the matrix of T is
[2 1]
[0 1]
Which means it has eigenvalues 2 and 1 with eigenvectors {1,0}. {1,-1}
Is that correct or did I misunderstadn something?
Thanks
Tal

Homework Equations

The Attempt at a Solution

 

[Mark44]

Homework Statement

The question si to find the jordan form of the following, I think it is diagnizable and am wondering if i am misunderstanding something or if diagnizable is a subccase of jordan form:
Anyway
Given the vector space $$R_1[x]$$ i.e. the space of linear functions (a+bx) find the jordan form of the follwoing matrix
$$T(a+bx)=2a+b+bx$$
I thinbk the matrix of T is
[2 1]
[0 1]
Which means it has eigenvalues 2 and 1 with eigenvectors {1,0}. {1,-1}
Is that correct or did I misunderstadn something?
Thanks
Tal

Everything looks fine, Tal. If you write P using your eigenvectors as columns, and find P^-1, P^-1AP is a diagonal matrix.

 

[talolard]

Thanks Mark