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The zero forcing number Z(G), which is the minimum number of vertices in azero forcing set of a graph G, is used to study the maximum nullity / minimumrank of the family of symmetric matrices described by G. It is shown that for aconnected graph of order at least two, no vertex is in every zero forcing set.The positive semidefinite zero forcing number Z_+(G) is introduced, and shownto be equal to |G|-OS(G), where OS(G) is the recently defined ordered setnumber that is a lower bound for minimum positive semidefinite rank. Thepositive semidefinite zero forcing number is applied to the computation ofpositive semidefinite minimum rank of certain graphs. An example of a graph forwhich the real positive symmetric semidefinite minimum rank is greater than thecomplex Hermitian positive semidefinite minimum rank is presented.

Zero forcing parameters and minimum rank problems