Motivated by the conjectures formulated in 2003 [28], we study interlacing properties of eigenvalues A⊗B+B⊗A for pairs n-by-n matrices A,B. We prove that every pair symmetric (and skew-symmetric matrices) with one them at most rank two, odd spectrum (those determined eigenvectors) interlaces its even eigenvectors). Using this result, also show when n≤3, The results specify structure eigenvector...

The tensor product, also called direct, categorical, or Kronecker product of graphs, is one of the least-understood graph products. In this paper we determine partial answers to the question given in the title, thereby significantly extending results of Broere and Hattingh (see [2]). We characterize completely those pairs of complete graphs whose tensor products are circulant. We establish that...

Two different descriptions are used in the literature to formulate the optimal dynamic output feedback control problem for linear dynamical systems with white stochastic parameters and quadratic criteria, called the optimal compensation problem. One describes the matrix valued white stochastic processes involved, using a sum of deterministic matrices each one multiplied by a scalar stochastic p...

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.

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...