Persymmetric and bisymmetric nonnegative inverse eigenvalue problem

The nonnegative inverse eigenvalue problem (NIEP  ) is the problem of finding conditions for the existence of an n×nn×n entrywise nonnegative matrix A   with prescribed spectrum. This problem remains open for n≥5n≥5. If the matrix A is required to be persymmetric (bisymmetric), the problem will be called persymmetric (bisymmetric) nonnegative inverse eigenvalue problem (PNIEP) (BNIEP). Persymmetric and bisymmetric matrices are common in physical sciences and engineering. They arise, for instance, in the control of mechanical and electric vibrations. A persymmetric version of a perturbation result, due to Rado and presented by H. Perfect in [5], is developed and used to give sufficient conditions for the PNIEP to have a solution. Our results generate an algorithmic procedure to compute the solution matrix.