In this paper, existence and uniqueness of solutions to two-point boundary value problem associated with the non-linear kronecker product Lyapunov system on time scales are derived. These generalize the results obtained for two-point boundary value problems involving kronecker products. Bartles-Stewart algorithm and a modified QR-algorithm are presented for solving the system of equations invol...

Leopardi introduced the notion of a Kronecker quotient in [Paul Leopardi. A generalized FFT for Clifford algebras. Bulletin of the Belgian Mathematical Society, 11:663–688, 2005.]. This article considers the basic properties that a Kronecker quotient should satisfy and additional properties which may be satisfied. A class of Kronecker quotients for which these properties have a natural descript...

In this paper, we investigate isomorphic factorizations of the Kronecker product graphs. Using these relations, it is shown that (1) the Kronecker product of the d-out-regular digraph and the complete symmetric digraph is factorized into the line digraph, (2) the Kronecker product of the Kautz digraph and the de Bruijn digraph is factorized into the Kautz digraph, (3) the Kronecker product of b...

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 ...

The displacement structure is extended to a Kronecker matrix W ⊗ Z. A new class of Kronecker-like matrices with the displacement rank r, r < n will be formulated and presented. The computational complexity of multiplication with vectors for Kronecker-like matrices has been accelerated. Applying the displacement, which was originally discovered by Kailath, Kung and Morf [15], a new superfast alg...

Real world graphs have been observed to display a number of surprising properties. These properties include heavy-tails for inand out-degree distributions, small diameters, and a densification law [5]. These features do not arise from the classical Erdos-Renyi random graph model [1]. To address these difficulties, Kronecker Graphs were first introduced in [5] as a new method of generating graph...

In this paper, first we convert the non-linear matrix Lyapunov system into a Kronecker product matrix system with the help of Kronecker product of matrices. Then, we obtain sufficient conditions for Ψasymptotic stability and Ψ-uniform stability of the trivial solutions of the corresponding Kronecker product system. c ©2012 NGA. All rights reserved.

This paper studies the properties of the Kronecker product related to the mixed matrix products, the vector operator, and the vecpermutation matrix and gives several theorems and their proofs. In addition, we establish the relations between the singular values of two matrices and their Kronecker product and the relations between the determinant, the trace, the rank, and the polynomial matrix of...

Stochastic Kronecker graphs are a model for complex networks where each edge is present independently according the Kronecker (tensor) product of a fixed matrix P ∈ [0, 1]k×k. We develop a novel correspondence between the adjacencies in a general stochastic Kronecker graph and the action of a fixed Markov chain. Using this correspondence we are able to generalize the arguments of Horn and Radcl...

—This paper presents a comparison between the outage capacity of MIMO channels predicted by the Kronecker and Müller models as a function of the number of scatterers, transmit and receive antennas. The Müller model is based on the single-scattered rays between arrays of transmit-and receive antennas, while the Kronecker model considers only double scattering. The channel capacity predictions by...