The Kronecker Product and Stochastic Automata Networks

This paper can be thought of as a companion paper to Van Loan's The Ubiquitous Kronecker Product paper [23]. 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 Loan's list of applications, namely Stochastic Automata Networks. Key words: Stochastic automata networks, Kronecker products, Kronecker product properties, Preconditioning