New data structures for representation of integer functions and matrices are proposed, namely, multiroot binary decision diagrams (MRBDD). Algorithms for performing standard operations on functions and matrices represented by MRBDDs are presented. Thanks to the more efficient reuse of structural elements, representation by multiroot binary decision diagrams is more efficient than the widely used multiterminal binary decision diagrams (MTBDD). Experimental results are given, which show that multiroot binary decision diagrams are a promising alternative to multiterminal binary decision diagrams, in particular, in probabilistic verification, manipulation of probability distributions, analysis of Petri nets, and other computational models.