  For a two-component bosonic system, the components can be mapped onto a
pseudo-spin degree of freedom with spin quantum number S=1/2. We provide a
rigorous proof that for a wide-range of real Hamiltonians with component
independent mass and interaction, the ground state is a ferromagnetic state
with pseudospin fully polarized. The spin-wave excitations are studied and
found to have quadratic dispersion relations at long wave length.
