We investigate yet another direct link between linear algebra and electronic structure theory by exploring the usefulness of the Gershgorin Theorem in the estimation of the correlation energies of many-particle systems. For a case study, we focus on a particular class of systems, two-dimensional quantum dots, and perform extensive numerical calculations by means of a 2p2h Configuration Interaction scheme. We find that the so-called Gershgorin radii constitute natural bounds for the correlation energy though –unfortunately– very loose bounds. However, we show that both quantities can be related through a scaling relation. This result opens the path to further investigations and has perspectives in the design of, e.g., highly parallelized algorithms. Furthermore, this conclusion applies only to two-dimensional (parabolic) quantum dots, and the situation might differ in different classes of systems. This possibility is left as an open question. \(^1\) (The initial exploration of Gershgorin bounds for electronic correlation was conducted by one of us (A.O.) during doctoral research. While many procedural aspects in the present study closely follow -for obvious reasons- the framework outlined in Sect. 3.1.1 of Ref. [1], the original analysis faced limitations due to inconsistencies in numerical convergence. As a result, a comprehensive review incorporating fully converged ground-state energies remained an open issue and was never formally published in paper format.)