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[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

form.

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?

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# 4 transformation matrices to jordan form

Can you offer guidance or do you also need help?

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