We study how to obtain partial matchings using the block function $\mathcal{M}_f$, induced by a morphism $f$ between persistence modules. $\mathcal{M}_f$ is defined algebraically and is linear with respect to direct sums of morphisms. We study some interesting properties of $\mathcal{M}_f$, and provide a way to obtain $\mathcal{M}_f$ using matrix operations.

翻译：我们研究如何利用由持续模之间同态$f$诱导的块函数$\mathcal{M}_f$获得部分匹配。$\mathcal{M}_f$以代数方式定义，并且关于同态的直和具有线性性质。我们探讨了$\mathcal{M}_f$的一些有趣性质，并提供了一种通过矩阵运算获取$\mathcal{M}_f$的方法。