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  "body": "\n## Statement\n\nLet $F$ be a field and let $A$ be an $n \\times n$ matrix over $F$.\nThen the [[minimal polynomial|03NDVCSHSB]] of $A$ divides the [[characteristic polynomial|0VSSPAFM2C]] of $A$.\nIn particular, $\\deg m_A \\le n$.\n\n## Remarks\n\nThe [[Cayley–Hamilton theorem|0F765KFC2J]] gives $p_A(A) = 0$, and the minimal polynomial divides each annihilating polynomial.\nThe characteristic polynomial divides a power of the minimal polynomial, because both have the same irreducible factors.\nFor $I_2$, $m = t - 1$ divides $p = (t - 1)^2$ and is not equal to it.\n\n## Explanations\n\n### L1 human\n\nThe minimal polynomial is a divisor of the characteristic polynomial.\nSo its degree is at most the size of the matrix.\nBoth polynomials have the same roots.\n",
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