  We present a general construction of pseudo-hermitian matrices in an
arbitrary large, but finite dimensional vector space. The positive-definite
metric which ensures reality of the entire spectra of a pseudo-hermitian
operator, and is used for defining a modified inner-product in the associated
vector space is also presented. The construction for an N dimensional vector
space is based on the generators of SU (N ) in the fundamental representation
and the identity operator. We apply the results to construct a generic
pseudo-hermitian lattice model of size N with balanced loss-gain. The system is
amenable to periodic as well as open boundary conditions and by construction,
admits entirely real spectra along with unitary time-evolution. The tight
binding and Su-Schrieffer-Heeger(SSH) models with nearest neighbour(NN) and
next-nearest neighbour(NNN) interaction with balanced loss-gain appear as
limiting cases.
