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  1. #1
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    jordan block question

    what is the difference between the jordan form of matrices A
    and diagonal block matrices similar to A
    ?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: jordan block question

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

    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}

    J is the Jordan form of A, K is a diagonal block matrix similar to A but it is not its Jordan form.
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  3. #3
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    Re: jordan block question

    because of the 2 ,3 on the smaller diagonal
    ?
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Re: jordan block question

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