Inverse spectral problem for an antisymmetric tridiagonal matrix

The problem of recovering an antisymmetric tridiagonal matrix from the eigenvalues of this matrix and the normalizing constants for its eigenvectors is solved. Matrices of this type arise in the theory of small oscillations of mechanical systems and are related to the matrices of the systems through the Schrödinger transformation. The problem is solved by the method of orthogonal polynomials.