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4 transformation matrices to jordan form

  1. Oct 28, 2011 #1
    [tex]A=\left(\begin{array}{cc}4 & -4\\1 & 0\end{array}\right)[/tex]
    find the jordan form and the transformation matrices P to this jordan
    the caracteristic and minimal polinomial is [tex]P(t)=M(t)=(t-2)^{2}[/tex]
    so the jordan form is [tex]J_{A}=\left(\begin{array}{cc}2 & 1\\0 & 2\end{array}\right)[/tex].
    my prof taught a method of finding the P
    he gave an example like if [tex]J_{B}=\left(\begin{array}{cc}0 & 1\\
    0 & 0\end{array}\right)[/tex]
    then we use chain method ,for the first column [tex]Tv_{1}=0[/tex] for the
    second its [tex]Tv_{2}=v_{1}[/tex]
    so [tex]v_{1}\in kerT[/tex] [tex]v_{2}\in kerT^{2}[/tex]
    i have two question:
    regarding the example of the prof [tex]kerT^{2}[/tex] is [tex]R^{2}[/tex] what vector
    to pick for [tex]v_{2}[/tex]?
    regarding my original example i have for the first coulumn of the
    jordan form [tex]Tv_{1}=2v_{1}[/tex] for the second [tex]Tv_{2}=v_{1}+2v_{2}[/tex]
    so i cant assosiate v\_1 and v\_2 with kernel of T
    i know that i can assosiate v1 with Ker(T-2I)
    but then i lose the chain method my prof taught.
    what to do?
  2. jcsd
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