The Jacobi ensemble is one of three ensembles of classical random matrix theory. It has a corresponding matrix form, so that a natural endeavor is to prove universality for the spectral properties of the matrix form. In joint work with L. Erdõs we provide the first such result. More interestingly, this matrix form has special relevance to other areas of mathematics because its eigenvalues describe the angles between random subspaces. We will consider random subspaces spanned by Euclidean and Fourier vectors and show how the Jacobi ensemble is related to discrete uncertainty principles.