  We investigate the isotropic two-leg S=1/2 ladder with general bilinear and
biquadratic exchange interactions between spins on neighboring rungs, and
determine the Hamiltonians which have a matrix product wavefunction as exact
ground state. We demonstrate that a smooth change of parameters leads one from
the S=1/2 dimer and Majumdar-Ghosh chains to the S=1 chain with biquadratic
exchange. This proves that these model systems are in the same phase. We also
present a new set of models of frustrated S=1/2 spin chains (including only
bilinear NN and NNN interactions) whose ground states can be found exactly.
