Many reported discovery systems build discrete models of hidden
structure, properties, or processes in the diverse fields of biology,
chemistry, and physics. We show that the search spaces underlying
many well-known systems are remarkably similar when re-interpreted as
search in matrix spaces. A small number of matrix types are used to
represent the input data and output models. Most of the constraints
can be represented as matrix constraints; most notably, conservation
laws and their analogues can be represented as matrix equations.
Typically, one or more matrix dimensions grow as these systems
consider more complex models after simpler models fail, and we
introduce a notation to express this. The novel framework of
matrix-space search serves to unify previous systems and suggests how
at least two of them can be integrated. Our analysis constitutes an
advance toward a generalized account of model-building in science.