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We present a general construction of pseudo-hermitian matrices in anarbitrary large, but finite dimensional vector space. The positive-definitemetric which ensures reality of the entire spectra of a pseudo-hermitianoperator, and is used for defining a modified inner-product in the associatedvector space is also presented. The construction for an N dimensional vectorspace is based on the generators of SU (N ) in the fundamental representationand the identity operator. We apply the results to construct a genericpseudo-hermitian lattice model of size N with balanced loss-gain. The system isamenable to periodic as well as open boundary conditions and by construction,admits entirely real spectra along with unitary time-evolution. The tightbinding and Su-Schrieffer-Heeger(SSH) models with nearest neighbour(NN) andnext-nearest neighbour(NNN) interaction with balanced loss-gain appear aslimiting cases.

Construction of Pseudo-hermitian matrices describing systems with balanced loss-gain