Controllability of Kronecker product networks

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,...

Shifted Kronecker Product Systems

Abstract. A fast method for solving a linear system of the form (A(p) ⊗ · · · ⊗ A(1) − λI)x = b is given where each A(i) is an ni-by-ni matrix. The first step is to convert the problem to triangular form (T (p) ⊗ · · · ⊗ T (1) − λI)y = c by computing the (complex) Schur decompositions of the A(i). This is followed by a recursive back-substitution process that fully exploits the Kronecker struct...

Transformation of the Kronecker Product

Block Kronecker Product Graph Model

Since Kronecker Product Graph Model (KPGM) was introduced, it has been widely used to model real networks. The characteristics of the model specially its single fractal structure have made KPGM one of the most important algorithm of the last years. However, the utilization of a single fractal structure decreases the potential of KPGM by limiting the graph space covered by the model. In this pap...

Kronecker product/Direct product/Tensor product in Quantum Theory

The properties and applications of kronecker product in quantum theory is studied thoroughly. The use of kronecker product in quantum information theory to get the exact spin Hamiltonian is given. The proof of non-commutativity of matrices, when kronecker product is used between them is given. It is shown that the non-commutative matrices after kronecker product are similar or they are similar ...