Jordan normal form

dear Professor,

I have a few questions regarding jordan canonical form, id be grateful if you could point me in the right direction…..im struggling to understand how you can work out Jordan form from the jordan basis…..e.g. if i have

Cha(X)= (x-2)^3
Ma(X)=(x-2)^2

and a Jordan basis of

B1={[1,0,3],[2,-3,0]}
B2={(1,0,0]}

how do i no what the JF is???

I no its…

2
2
2

[along the diagonal]

but what goes in the gaps, ie the 1’s

Reply:

Check the Jordan basis carefully. But you don’t need it to calculate the JNF in this case. The minimal polynomial tells you that the size of the largest Jordan block is 2×2. Think about that a bit.

MK

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