The inverse eigenvalue problem for symmetric anti-bidiagonal matrices

The inverse eigenvalue problem for real symmetric matrices of the form000⋯00∗000⋯0∗∗000⋯∗∗0·⋮⋮⋮·⋮⋮⋮·00∗⋯0000∗∗⋯000∗∗0⋯000is solved. The solution is shown to be unique. The problem is also shown to be equivalent to the inverse eigenvalue problem for a certain subclass of Jacobi matrices.