  We study the singular values of certain triangular random matrices. When
their elements are i.i.d. standard complex Gaussian random variables, the
squares of the singular values form a biorthogonal ensemble, and with an
appropriate change in the distribution of the diagonal elements, they give the
biorthogonal Laguerre ensemble. For triangular Wigner matrices, we give
alternative proofs for the convergence of the empirical distribution of the
appropriately scaled squares of the singular eigenvalues to a distribution with
support $[0, e]$, as well as for the almost sure convergence of the rescaled
largest singular eigenvalue to $\sqrt{e}$ under the additional assumption of
mean zero and finite fourth moment for the law of the matrix elements.
