Lie biderivations on a generalized matrix algebra

In this paper, we investigate the structure of Lie biderivations on a generalized matrix algebra $\mathcal{G}$. Although results on Lie biderivations are well-established for triangular algebras, the extension to the broader class of generalized matrix algebras has remained largely unexplored, and our work fills this gap. By leveraging the faithful bimodule structure of $\mathcal{G}$, we prove that, under mild conditions, every Lie biderivation on $\mathcal{G}$ can be decomposed into the sum of a biderivation and a central mapping. As a direct application, we extend this result to obtain an analogous decomposition for Lie biderivations on full matrix algebras.