Good evening,
I would love your help with this.
I want to know what's jordan normal form of matrix that it's $Characteristic$ $ $ $polynomial$ : $(t-3)^{4}\cdot (t-5)^{4}$
and it's $Minimal$ $ $ $ polynomial$ : $(t-3)^{2}\cdot (t-5)^{2}$.
I believe that these are the options:
$J_{A}=diag(J_{2}(3),J_{2}(3),J_{2}(5),J_{2}(5))$,
$J_{A}=diag(J_{2}(3),J_{2}(3),J_{2}(5),J_{1}(5),J_{1}(5))$,
$J_{A}=diag(J_{2}(3),J_{1}(3),J_{1}(3),J_{2}(5),J_{1}(5),J_{1}(5))$,
$J_{A}=diag(J_{2}(3),J_{1}(3),J_{1}(3),J_{2}(5),J_{2}(5))$.
My Question are:
1.Am I right?
2.Was there any difference if Jordan matrices of eigenvalue 5 were before eigenvalue 3? and why?
3.Is there any way to know more about what is the specific jordan normal form with this information?
Thank you guys.