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Characteristic and minimal polynomials

Created over 8 years ago, updated 10 days ago

The 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).