In this paper, we study how basis-independent partial matchings induced by morphisms between persistence modules (also called ladder modules) can be defined. Besides, we extend the notion of basis-independent partial matchings to the situation of a pair of morphisms with same target persistence module. The relation with the state-of-the-art methods is also given. Apart form the basis-independent property, another important property that makes our partial matchings different to the state-of-the-art ones is their linearity with respect to ladder modules.
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