  It is generally believed that Parity-Time (PT)-symmetry breaking occurs when
eigenvalues or both eigenvalues and eigenvectors coincide. However, we show
that this well-accepted picture of PT-symmetry breaking is incorrect. Instead,
we demonstrate that the physical mechanism of PT-symmetry breaking is the
resonance between positive- and negative-action modes. It is proved that
PT-symmetry breaking occurs when and only when this resonance condition is
satisfied, and this mechanism applies to all known PT-symmetry breakings
observed in different branches of physics. The result is achieved by proving a
remarkable fact that in finite dimensions, a PT-symmetric Hamiltonian is
necessarily pseudo-Hermitian, regardless whether it is diagonalizable or not.
