Related papers: Nuclear Norm Under Tensor Kronecker Products
We extend the classical Mercer theorem to reproducing kernel Hilbert spaces whose elements are functions from a measurable space $X$into $\mathbb C^n$. Given a finite measure $\mu$ on $X$, we represent the reproducing kernel $K$ as…
Tensor Kronecker products, the natural generalization of the matrix Kronecker product, are independently emerging in multiple research communities. Like their matrix counterpart, the tensor generalization gives structure for implicit…
The theory of tensor categories has found applications across various fields, including representation theory, quantum field theory (conformal in 2 dimensions, and topological in 3 and 4 dimensions), quantum invariants of low-dimensional…
An invertible matrix is called a Perron similarity if one of its columns and the corresponding row of its inverse are both nonnegative or both nonpositive. Such matrices are of relevance and import in the study of the nonnegative inverse…
We study strongly graded vertex algebras and their strongly graded modules, which are conformal vertex algebras and their modules with a second, compatible grading by an abelian group satisfying certain grading restriction conditions. We…
We find a necessary and sufficient condition for the existence of the tensor product of modules over a Lie conformal algebra. We provide two algebraic constructions of the tensor product. We show the relation between tensor product and…
In a categorification of tensor products of fundamental representations of quantum sl(k) via highest weight categories, the indecomposable tilting modules descend to the canonical basis. Since projective functors map tilting modules to…
We illustrate a counterexample to an open question related to the dominant H-eigenvector of a Kronecker product of tensors. For matrices and Z-eigenvectors of tensors, the dominant eigenvector of a Kronecker product decouples into a product…
In this note, inspired by the proof of the Kirillov-Reshetikhin conjecture, we consider tensor products of Kirillov-Reshetikhin modules of a fixed node and various level. We fix a positive integer and attach to each of its partitions such a…
A concept of multiplicator of symmetric function space concerning to projective tensor product is introduced and studied. This allows to obtain some concrete results. In particular, the well-known theorem of R. O'Neil about the boundedness…
The properties and applications of kronecker product in quantum theory is studied thoroughly. The use of kronecker product in quantum information theory to get the exact spin Hamiltonian is given. The proof of non-commutativity of matrices,…
Recently, low-rank tensor completion has become increasingly attractive in recovering incomplete visual data. Considering a color image or video as a three-dimensional (3D) tensor, existing studies have put forward several definitions of…
Since Kilmer et al. introduced the new multiplication method between two third-order tensors around 2008 and third-order tensors with such multiplication structure are also called as T-product tensors, T-product tensors have been applied to…
Currently, low-rank tensor completion has gained cumulative attention in recovering incomplete visual data whose partial elements are missing. By taking a color image or video as a three-dimensional (3D) tensor, previous studies have…
Controlling the spectral norm of the Jacobian matrix, which is related to the convolution operation, has been shown to improve generalization, training stability and robustness in CNNs. Existing methods for computing the norm either tend to…
We present a new kind of normalization theorem: linearization theorem for skew products. The normal form is a skew product again, with the fiber maps linear. It appears, that even in the smooth case, the conjugacy is only H\"older…
We study right exact tensor products on the category of finitely presented functors. As our main technical tool, we use a multilinear version of the universal property of so-called Freyd categories. Furthermore, we compare our constructions…
We compute the determinant of $\sum_{n=1}^{N} \vec{A}^{(n)} \otimes \vec{B}^{(n)}$, where $\vec{A}^{(n)}$ is square and ${\vec{B}^{(n)}=\vec{x}^{(n)}{\vec{y}^{(n)}}^T}$ where $\vec{x}^{(n)}$ and $\vec{y}^{(n)}$ have length $N$.
New bounds are derived for the eigenvalues of sums of Kronecker products of square matrices by relating the corresponding matrix expressions to the covariance structure of suitable bi-linear stochastic systems in discrete and continuous…
A Kronecker coefficient is the multiplicity of an irreducible representation of a finite group $G$ in a tensor product of irreducible representations. We define Kronecker Hecke algebras and use them as a tool to study Kronecker coefficients…