The Kronecker product and stochastic automata networks

This paper can be thought of as a companion paper to Van Loanʹs The Ubiquitous Kronecker Product paper (J. Comput. Appl. Math. 123 (2000) 85). We collect and catalog the most useful properties of the Kronecker product and present them in one place. We prove several new properties that we discovered in our search for a stochastic automata network preconditioner. We conclude by describing one application of the Kronecker product, omitted from Van Loanʹs list of applications, namely stochastic automata networks.