  The two-by-two Sp(2) matrix has three parameters with unit determinant. Yet,
there are no established procedures for diagonalizing this matrix. It is shown
that this matrix can be written as a similarity transformation of the
two-by-two Wigner matrix, derivable from Wigner's little group which dictates
the internal space-time symmetries of relativistic particles. The Wigner matrix
can be diagonalized for massive and space-like particles, while it takes a
triangular form with unit diagonal elements for light-like particles. The most
immediate physical application can be made to repeated one-dimensional transfer
matrices appearing in many different branches of physics. Another application
of current interest could be the dis-entanglement of entangled systems.
