One-dimensional persistent homology encodes geometric information of data by means of a barcode decomposition. Often, one needs to relate the persistence barcodes of two datasets which are intrinsically linked, e.g. consider a sample from a large point cloud. Such connections are encoded through persistence morphisms; as in linear algebra, a (one-dimensional) persistence morphism is fully understood by fixing a basis in the domain and codomain and computing the associated matrix. However, in the literature and existing software, the focus is often restricted to interval decompositions of images, kernels and cokernels. This is the case of the Bauer-Lesnick matching, which is computed using the intervals from the image. Unfortunately, this matching has substantial differences from the structure of the persistence morphism in very simple examples. In this talk I will present an induced block function that is well-behaved in such examples. This block function is computed using the associated matrix of a persistence morphism and is additive with respect to taking direct sums of persistence morphisms. This is joint work with M. Soriano-Trigueros and R. Gonzalez-Díaz from Universidad de Sevilla.