Using the block vec matrix, I give a necessary and sufficient condition for factorization of a matrix into the Kronecker product of two other matrices. As a consequence, I obtain an elementary algorithmic procedure to decide whether a matrix has a square root for the Kronecker product. Introduction My statistician colleague, J.E. Chacón, asked me how to decide if a real given matrix A has a squ...

This contribution proposes a decompositional iterative method for the steadystate analysis of Kronecker structured Markov chains [1]. The Markovian system, which is formed by a composition of subsystems using the Kronecker sum operator for local transitions and the Kronecker product operator for synchronized transitions, is assumed to have irreducible subsystem matrices associated with local tr...

We present combinatorial operators for the expansion of the Kronecker product of irreducible representations of the symmetric group Sn. These combinatorial operators are defined in the ring of symmetric functions and act on the Schur functions basis. This leads to a combinatorial description of the Kronecker powers of the irreducible representations indexed with the partition (n− 1, 1) which sp...

In this paper, the effect of spatial smoothing on performance of widely used stochastic narrowband multiple-input multiple-output (MIMO) radio channel model, namely the Kronecker model, is investigated based on data measured in urban microcellular environment at 5.3 GHz carrier frequency. Results from non-line of sight (NLOS) and line of sight (LOS) traveling routes are analyzed. It is noticed ...

We propose the tensor Kronecker product singular value decomposition (TKPSVD) that decomposes a real k-way tensor A into a linear combination of tensor Kronecker products with an arbitrary number of d factors A = ∑R j=1 σj A (d) j ⊗ · · · ⊗ A (1) j . We generalize the matrix Kronecker product to tensors such that each factor A j in the TKPSVD is a k-way tensor. The algorithm relies on reshaping...

Given a large, real graph, how can we generate a synthetic graph that matches its properties, i.e., it has similar degree distribution, similar (small) diameter, similar spectrum, etc? We propose to use “Kronecker graphs”, which naturally obey all of the above properties. We present a fast linear time algorithm for fitting the Kronecker graph generation model to real networks. Experiments on la...

A new solution technique is proposed for linear systems with large dense matrices of a certain class including those that come from typical integral equations of potential theory. This technique combines Kronecker product approximation and wavelet sparsification for the Kronecker product factors. The user is only required to supply a procedure for computation of each entry of the given matrix. ...

We propose a computationally efficient and numerically reliable algorithm to compute Kronecker-like forms of periodic matrix pairs. The eigenvalues and Kronecker indices are defined via the Kro-necker structure of an associated lifted matrix pencil. The proposed reduction method relies on structure preserving manipulations of this pencil to extract successively lower complexity subpencils which...