1. ## jordan block question

what is the difference between the jordan form of matrices A
and diagonal block matrices similar to A
?

2. ## Re: jordan block question

Originally Posted by transgalactic
what is the difference between the jordan form of matrices A and diagonal block matrices similar to A?
Difference, in what terms? For example

$\displaystyle A\sim J=\begin{bmatrix}{\lambda}&{1}&{0}\\{0}&{\lambda}& {1}\\{0}&{0}&{\lambda}\end{bmatrix}\Rightarrow A\sim K=\begin{bmatrix}{\lambda}&{2}&{0}\\{0}&{\lambda}& {3}\\{0}&{0}&{\lambda}\end{bmatrix}$

$\displaystyle J$ is the Jordan form of $\displaystyle A$, $\displaystyle K$ is a diagonal block matrix similar to $\displaystyle A$ but it is not its Jordan form.

3. ## Re: jordan block question

because of the 2 ,3 on the smaller diagonal
?

4. ## Re: jordan block question

Originally Posted by transgalactic
because of the 2 ,3 on the smaller diagonal?
It is irrelevant, only an example. The important thing is that $\displaystyle \dim \ker (K-\lambda I)=1$ so, the Jordan form of $\displaystyle K$ is $\displaystyle J$ .