This paper uses unit lower triangular matrices to solve the nonnegative inverse eigenvalue problem for various sets of real numbers. This problem has remained unsolved for many years for n ≥ 5. The inverse of the unit lower triangular matrices can be easily calculated and the matrix similarities are also helpful to be able to solve this important problem to a considerable extent. It is assumed that in the given set of eigenvalues, the number of positive eigenvalues is less than or equal to the number of nonpositive eigenvalues to find a nonnegative matrix such that the given set is its spectrum.
