Let $A\in M_n(\mathbb{C})$. The minimal polynomial of $A$ is $m_A = x^6 - 4x^4+3x^2 +1$. What is the minimal polynomial of $A^2$?
I'd be glad for an hint/direction.
Thanks!
2026-04-18 02:53:41.1776480821
What is the minimal polynomial of $A^2$?
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There is an obvious cubic polynomial that $A^2$ satisfies. (Don't worry that $A$ is a matrix.) If $A^2$ satisfied a smaller polynomial than a cubic, then $A$ would satisfy a smaller polynomial than a degree 6.