The understanding of which Kronecker structures that are close to a given structure is revealed by the Kronecker structure hierarchy, i.e., the strati cation of the Kronecker canonical form. For a given matrix pencil A B, the Kronecker structure hierarchy shows all structures that are within the closure of orbit(A B), and each structure, whose orbit's closure contains A B. In order to gain new ...

in this paper we define ?-independent (a weak-version of independence), kronecker and dissociate sets on hypergroups and study their properties and relationships among them and some other thin sets such as independent and sidon sets. these sets have the lacunarity or thinness property and are very useful indeed. for example varopoulos used the kronecker sets to prove the malliavin theorem. in t...

We consider the problem of recovering a low-rank tensor from its noisy observation. Previous work has shown a recovery guarantee with signal to noise ratio O(ndK/2e/2) for recovering a Kth order rank one tensor of size n × · · · × n by recursive unfolding. In this paper, we first improve this bound to O(n) by a much simpler approach, but with a more careful analysis. Then we propose a new norm ...

In recent years, a number of results on Kronecker products of complex Sncharacters have been obtained. In particular, the rectangular hull for the constituents in such products was found, and this was used for the classification of products with few homogeneous components; see [1] for this classification result and references to related work. Here, we provide similar results for products of spi...

Many image processing applications require computing approximate solutions of very large, ill-conditioned linear systems. Physical assumptions of the imaging system usually dictate that the matrices in these linear systems have exploitable structure. The specific structure depends on (usually simplifying) assumptions of the physical model and other considerations such as boundary conditions. Wh...

Stochastic Kronecker Product Graphs are an interesting and useful class of Generative Network Models. They can be fitted using a fast Maximum Likelihood Estimator and reproduce many important statistical properties commonly found in large real-world networks. However, they suffer from an unfortunate drawback: the need to pad the Stochastic Kronecker Product Graph with isolated vertices. To addr...

We show that the Kronecker coefficients indexed by two two–row shapes are given by quadratic quasipolynomial formulas whose domains are the maximal cells of a fan. Simple calculations provide explicitly the quasipolynomial formulas and a description of the associated fan. These new formulas are obtained from analogous formulas for the corresponding reduced Kronecker coefficients and a formula r...