We consider the conditions under which the Cayley transform of the Kronecker product of two Hermitian matrices can be again presented as a Kronecker product of two matrices and, if so, if it is a product of the Cayley transforms of the two Hermitian matrices. 2010 Math. Subj. Class.: 15A69, 15B57.

In this note we make explicit a stability property for Kronecker coefficients that is implicit in a theorem of Y. Dvir. Even in the simplest nontrivial case this property was overlooked despite of the work of several authors. As applications we give a new vanishing result and a new formula for some Kronecker coefficients.

In this paper, we construct p-adic analogues of the Kronecker double series, which we call the Eisenstein-Kronecker series, as Coleman functions on an elliptic curve with complex multiplication. We then show that the periods of the specialization of the p-adic elliptic polylogarithm sheaf to arbitrary non-zero points of the elliptic curve may be expressed using these functions.

Strong Kronecker multiplication of two matrices is useful for constructing new orthogonal matrices from those known. These results are particularly important as they allow small matrices to be combined to form larger matrices, but of smaller order than the straight-forward Kronecker product would permit.

Three properties of matrices: the spark, the mutual incoherence and the restricted isometry property have recently been introduced in the context of compressed sensing. We study these properties for matrices that are Kronecker products and show how these properties relate to those of the factors. For the mutual incoherence we also discuss results for sums of Kronecker products.

Confirming a conjecture made by Bessenrodt and Kleshchev in 1999, we classify all Kronecker products of characters of the symmetric groups with only three or four components. On the way towards this result, we obtain new information about constituents in Kronecker products.

In this paper, we propose and study a technique to reduce the number of parameters and computation time in convolutional neural networks. We use Kronecker product to exploit the local structures within convolution and fully-connected layers, by replacing the large weight matrices by combinations of multiple Kronecker products of smaller matrices. Just as the Kronecker product is a generalizatio...

In kernel machines, such as kernel principal component analysis (KPCA), Gaussian Processes (GPs), and Support Vector Machines (SVMs), the computational complexity of finding a solution is O(n), where n is the number of training instances. To reduce this expensive computational complexity, we propose using Kronecker factorization, which approximates a positive definite kernel matrix by the Krone...