variables $s, t$ with coefficients in ${\mathbb F}$. We denote by ${\mathbb F}^{p\times q}$, ${\mathbb F}[s]^{p\times q}$ and ${\mathbb F}[s, t]^{p\times q}$ the vector spaces of $p\times q$ matrices with elements in ${\mathbb F}$, ${\mathbb F}[s]$ and ${\mathbb F}[s, t]$, respectively. $\Gl_p({\mathbb F})$ will be the general linear group of invertible matrices in ${\mathbb F}^{p \times p}$.

Given a polynomial matrix $G(s)\in {\mathbb F}[s]^{p\times q}$, the [*degree*]{} of $G(s)$, denoted by $\deg(G(s))$, is the maximum of the degrees of its entries. The [*normal rank*]{} of $G(s)$, denoted by $\rank (G(s))$, is the order of the largest nonidentically zero minor of $G(s)$, i.e., it is the rank of $G(s)$ considered as a matrix on the field of fractions of ${\mathbb F}[s]$.

A [*matrix pencil*]{} is a polynomial matrix $G(s)\in {\mathbb F}[s]^{p\times q}$ such that $\deg(G(s))\leq1$. The pencil is [*regular*]{} if $p=q$ and $\det(G(s))$ is not the zero polynomial. Otherwise it is [*singular*]{}.

Two matrix pencils $G(s)=G_0+sG_1, H(s)=H_0+sH_1\in {\mathbb F}[s]^{p\times q}$ are [*strictly equivalent*]{} ($G(s){\ensuremath{\stackrel{s.e.}{\sim}}}H(s)$) if there exist invertible matrices $Q\in \Gl_p({\mathbb F})$, $R\in \Gl_q({\mathbb F})$ such that $G(s)=QH(s)R$.

Given the pencil $G(s)=G_0+sG_1 \in {\mathbb F}[s]^{p\times q}$ of $\rank G(s)=n$, a complete system of invariants for the strict equivalence of matrix pencils 