  The goal of this paper is to gather and develop some necessary and sufficient
criteria for injectivity and multistationarity in vector fields associated with
a chemical reaction network under a variety of more or less general assumptions
on the nature of the network and the reaction rates. The results are primarily
linear algebraic or matrix-theoretic, with some graph-theoretic results also
mentioned. Several results appear in, or are close to, results in the
literature. Here, we emphasise the connections between the results, and where
possible, present elementary proofs which rely solely on basic linear algebra
and calculus. A number of examples are provided to illustrate the variety of
subtly different conclusions which can be reached via different computations.
In addition, many of the computations are implemented in a web-based open
source platform, allowing the reader to test examples including and beyond
those analysed in the paper.
