= Annihilating polynomial
{title2=$p(A)=0$}
An <annihilating polynomial> of a <linear operator> is a nonzero polynomial $p$ for which the displayed operator is zero. The <minimal polynomial> is its unique monic annihilating polynomial of least degree and divides every other annihilating polynomial. For a diagonalizable operator with distinct eigenvalues $\lambda_1,\ldots,\lambda_s$, the product $\prod_j(t-\lambda_j)$ annihilates it. For an individual vector it suffices to annihilate the eigenvalues contributing to that vector; this gives exact finite-step termination bounds for a <Krylov subspace method>.
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