# Characteristic and minimal polynomials

Put content hereThe **characteristic polynomial** of $A$ is $p(\lambda) = \det(A - \lambda I)$. Its roots are the eigenvalues. The **minimal polynomial** $m(\lambda)$ is the monic polynomial of least degree such that $m(A) = 0$. The minimal polynomial divides the characteristic polynomial and has the same roots (but possibly with lower multiplicities).

# Parents

* Eigenvalues and eigenvectors