Could anyone help me to show how these two statements are equivalent?
$(1)$ rank $\begin{bmatrix}\lambda I-Y\\X\end{bmatrix}=n\forall \lambda\in \mathbb{C}$
$(2)$ For any monic polynomial $p(\lambda)=\lambda^n+a_1\lambda^{n-1}+\dots+a_n,a_i\in\mathbb{R},\exists$ a matrix with constant entries $M$ such that $\det(\lambda I-Y+MX)=p(\lambda)$
given, $M$ is $n\times p$, $Y$ is $n\times n$, and $X$ is $p\times n$