The strong Kronecker product

Transformation 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...

Some Applications of Strong Product

Let G and H be graphs. The strong product GH of graphs G and H is the graph with vertex set V(G)V(H) and u=(u1, v1) is adjacent with v= (u2, v2) whenever (v1 = v2 and u1 is adjacent with u2) or (u1 = u2 and v1 is adjacent with v2) or (u1 is adjacent with u2 and v1 is adjacent with v2). In this paper, we first collect the earlier results about strong product and then we present applications of ...

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...

Entangled Quantum States and the Kronecker Product

Entangled quantum states are an important component of quantum computing techniques such as quantum error-correction, dense coding and quantum teleportation. We determine the requirements for a state in the Hilbert space C C for N to be entangled and a solution to the corresponding “factorization” problem if this is not the case. We consider the implications of these criteria for computer algeb...