A [[Polynomial]] equation for a [[Matrix]] whose solutions are all [[Eigenvalue|Eigenvalues]] of the [[Matrix]]. $\huge \det(A-tI)=0 $ $\huge c_{0}+c_{1}t+ \dots + c_{n}x^n = 0 $ $\huge x =\set {\lambda_{0}, \dots, \lambda_{i}} $ The [[Characteristic Polynomial]] of a [[Square]] $n\times n$ [[Matrix]] will always be of degree $n$. #### Leading Terms For some [[Matrix]] $A\in M_{n\times n}$ $\begin{align} \det(A-\lambda I) &= (-1)^n\lambda^n - (-1)^n\op{tr}(A)\lambda^{n-1}+\cdots \det(A) \\ \lambda &\in \C \end{align} $