The Ginibre ensemble is a mathematical concept in random matrix theory, specifically dealing with non-Hermitian matrices. It consists of matrices whose entries are independent and identically distributed complex Gaussian random variables. This ensemble is significant for studying the statistical properties of eigenvalues in complex systems. In the Ginibre ensemble, the eigenvalues are distributed in the complex plane, and their behavior can be analyzed using tools from probability theory and complex analysis. The ensemble is named after Jean Ginibre, who introduced it in the 1960s, and it serves as a foundational model for understanding more complex random matrix ensembles.