Kronecker or inner tensor products of representations of symmetric groups (and many other groups) have been studied for a long time. But even for the symmetric groups no reasonable formula for decomposing Kronecker products of two irreducible complex representations into irreducible components is available (cf. [7, 5]). An equivalent problem is to decompose the inner product of the correspondin...

In this paper, we consider the problem of recovering an unknown sparse matrix X from the matrix sketch Y = AXB . The dimension of Y is less than that of X, and A and B are known matrices. This problem can be solved using standard compressive sensing (CS) theory after converting it to vector form using the Kronecker operation. In this case, the measurement matrix assumes a Kronecker product stru...

The infinitesimal generator matrix underlying a multidimensional Markov chain can be represented compactly by using sums of Kronecker products of small rectangular matrices. For such compact representations, analysis methods based on vector-Kronecker product multiplication need to be employed. When the factors in the Kronecker product terms are relatively dense, vectorKronecker product multipli...

Pairwise classification has many applications including network prediction, entity resolution, and collaborative filtering. The pairwise kernel has been proposed for those purposes by several research groups independently, and become successful in various fields. In this paper, we propose an efficient alternative which we call Cartesian kernel. While the existing pairwise kernel (which we refer...

Measurements taken at the campus of Brigham Young University (BYU) are used to investigate the statistical properties of the indoor MIMO channel. Two statistical tests, Royston’s and HenzeZirkler’s, are applied to the MIMO data to assess whether the data belongs to a multivariate normal distribution or not. The possibility of modeling the covariance matrix as a Kronecker product of the correlat...

Kronecker product kernel provides the standard approach in the kernel methods' literature for learning from graph data, where edges are labeled and both start and end vertices have their own feature representations. The methods allow generalization to such new edges, whose start and end vertices do not appear in the training data, a setting known as zero-shot or zero-data learning. Such a setti...

The paper provides a generalization of our previous algorithm for the parallel multiplication of a vector by a Kronecker product of matrices. For any p, a factor of the problem size, our algorithm runs on p processors with a minimum number of communication steps and memory space. Specifically, on p processors with global communication, we show that the multiplication requires at least Θ(log(p))...

The Kronecker product of two homogeneous symmetric polynomials P1 and P2 is defined by means of the Frobenius map by the formula P1 ⊗ P2 = F (F−1P1)(F−1P2). When P1 and P2 are Schur functions sλ and sμ respectively, then the resulting product sλ ⊗ sμ is the Frobenius characteristic of the tensor product of the irreducible representations of the symmetric group corresponding to the diagrams λ an...

The Khatri-Rao and Tracy-Singh products for partitioned matrices are viewed as generalized Hadamard and generalized Kronecker products, respectively. We define the KhatriRao and Tracy-Singh sums for partitioned matrices as generalized Hadamard and generalized Kronecker sums and derive some results including matrix equalities and inequalities involving the two sums. Based on the connection betwe...

Convention: Let A be a T×m matrix; the notation vec(A) will mean the Tmelement column vector whose first set of T elements are the first colum of A, that is a.1 using the dot notation for columns; the second set of T elements are those of the second column of A, a.2, and so on. Thus A = [a.1, a.2, · · · , a.m] in the dot notation. An immediate consequences of the above Convention is Vec of a pr...