The Cayley–Hamilton identity is $p_A(A)=0$, where $p_A(t)=\det(tI-A)$. Example: for $A=\begin{bmatrix}1&1\\0&2\end{bmatrix}$, $p_A(t)=t^2-3t+2$ and $A^2-3A+2I=0$. This identity reduces high powers to combinations of $I,A,\ldots,A^{n-1}$.
Like how this is organised?
Build your own knowledge tree on knowen.md: notes, decisions and tasks in one connected markdown graph, shared with your team and your AI agents.