Sentence:  Each root of the <WSD>minimal polynomial</WSD> of a matrix M is an eigenvalue of M and a root of its characteristic polynomial. (A root of the <WSD>minimal polynomial</WSD> has a multiplicity that is less than or equal to the multiplicity of the same root in the characteristic polynomial. Thus the <WSD>minimal polynomial</WSD> divides the characteristic polynomial. Also, any root of the characteristic polynomial is also a root of the <WSD>minimal polynomial</WSD>, so the two kinds of polynomial have the same roots, only (possibly) differing in their multiplicities.) 
Meaning of the word marked with <WSD> tags:  For a given square matrix "M" over some field "K", the smallest-degree monic polynomial over "K" which, when applied to "M", yields the zero matrix.