  Let $\mathcal{G}$ be a generalized matrix algebra over a commutative ring
$\mathcal{R}$, ${\mathfrak q}\colon \mathcal{G}\times\mathcal{G}\longrightarrow
\mathcal{G}$ be an $\mathcal{R}$-bilinear mapping and ${\mathfrak T}_{\mathfrak
q}\colon:\mathcal{G}\longrightarrow \mathcal{G}$ be a trace of $\mathfrak{q}$.
We describe the form of ${\mathfrak T}_{\mathfrak q}$ satisfying the condition
${\mathfrak T}_{\mathfrak q}(G)G=G{\mathfrak T}_{\mathfrak q}(G)$ for all $G\in
\mathcal{G}$. The question of when ${\mathfrak T}_{\mathfrak q}$ has the proper
form is considered. Using the aforementioned trace function, we establish
sufficient conditions for each Lie isomorphism of $\mathcal{G}$ to be almost
standard. As applications we characterize Lie isomorphisms of full matrix
algebras, of triangular algebras and of certain unital algebras with nontrivial
idempotents. Some further research topics related to current work are proposed
at the end of this article.
