  Many one-dimensional lattice particle models with open boundaries, like the
paradigmatic Asymmetric Simple Exclusion Process (ASEP), have their stationary
states represented in the form of a matrix product, with matrices that do not
explicitly depend on the lattice site. In contrast, the stationary state of the
open one-dimensional Zero-Range Process (ZRP) takes an inhomogeneous factorized
form, with site-dependent probability weights. We show that in spite of the
absence of correlations, the stationary state of the open ZRP can also be
represented in a matrix product form, where the matrices are site-independent,
non-commuting and determined from algebraic relations resulting from the master
equation. We recover the known distribution of the open ZRP in two different
ways: first, using an explicit representation of the matrices and boundary
vectors; second, from the sole knowledge of the algebraic relations satisfied
by these matrices and vectors. Finally, an interpretation of the relation
between the matrix product form and the inhomogeneous factorized form is
proposed within the framework of hidden Markov chains.
