The notion of persistence partial matching, as a generalization of partial
matchings between persistence modules, is introduced. We study how to obtain a
persistence partial matching Gf, and a partial matching
Mf, induced by a morphism f between persistence modules, both
being linear with respect to direct sums of morphisms. Some of their properties
are also provided, including their stability after a perturbation of the
morphism f, and their relationship with other induced partial matchings
already defined in TDA