One of the most famous results in random matrix theory is the eigenvalue distribution of the Gaussian Unitary Ensemble (GUE). In this talk, I will briefly introduce GUE matrices and then present a tridiagonal matrix ensemble that shares the same eigenvalue distribution as GUE. These tridiagonal matrices are very handy because they provide a more computationally efficient way to model the eigenvalues of GUE. This expository talk aims to be accessible to graduate students without prior knowledge of random matrix theory. There will be a related talk next week by Han Le, who will present a more detailed application of tridiagonal random matrices. Speaker(s): Elizabeth Collins-Woodfin (University of Michigan)