Determine all possible Jordan forms of a linear transformation with characteristic polynomial $(x−2)^4(x−3)^3$ and minimal polynomial $(x−2)^2(x−3)^2$.
2026-03-26 22:58:21.1774565901
If we're given characteristic and minimal polynomial of a linear transformation, how can we find all its possible Jordan forms?
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Hint: The exponent of $(x - \lambda)$ in the characteristic polynomial is the sum of the sizes of the Jordan blocks associated with $\lambda$. The exponent of $(x - \lambda)$ in the minimal polynomial is the maximum among the sizes of the Jordan blocks associated with $\lambda$.