Sentence:  In this section we will show that if \{A, B, C, D\} is a controllable and observable realization of \mathbf G, then \lambda is a pole of \mathbf G if and only if \lambda is an eigenvalue of A. Moreover, the roots (multiplicities included) of the <WSD>minimal polynomial</WSD> of A are the poles of \mathbf G. 
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.