Uniqueness of the surface-wave spped: A proof that is independent of the Stroh formalism

It is well-known in surface-wave theory that the secular equation for the surface-wave speed v can be written as det M = 0 in terms of the surface impedance matrix M. It has recently been shown by the present authors that M satisfies a simple algebraic Riccati equation. It is shown in the present paper that a purely matrix algebraic analysis of this equation suffices to prove that whenever a surface wave exists it is unique.