Related papers: Symmetric Kronecker products and semiclassical wav…
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…
Kronecker products of unitary Fourier matrices play important role in solving multilevel circulant systems by a multidimensional Fast Fourier Transform. They are also special cases of complex Hadamard (Zeilinger) matrices arising in many…
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,…
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…
We review the properties of the Kronecker (direct, or tensor) product of square matrices $A \otimes B \otimes C \cdots$ in terms of Hubbard operators. In its simplest form, a Hubbard operator $X_n^{i,j}$ can be expressed as the $n$-square…
In this rather brief note we present and discuss techniques for solving Kronecker matrix product least squares problems. Our main contribution is an iterative approach that uses the efficient Kronecker matrix-vector multiplication strategy…
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…
In a recent paper, the authors introduced a new basis of the ring of symmetric functions which evaluate to the irreducible characters of the symmetric group at roots of unity. The structure coefficients for this new basis are the stable…
Hypergraphs and tensors extend classic graph and matrix theory to account for multiway relationships, which are ubiquitous in engineering, biological, and social systems. While the Kronecker product is a potent tool for analyzing the…
We apply symmetric function theory to study random processes formed by singular values of products of truncations of Haar distributed symplectic and orthogonal matrices. These product matrix processes are degenerations of Macdonald…
Kronecker product covariance structure provides an efficient way to modeling the inter-correlations of matrix-variate data. In this paper, we propose testing statistics for Kronecker product covariance matrix based on linear spectral…
We study two new families of symmetric functions arising from a species-theoretic construction motivated by cycle structure. For each partition of $n$, we define two combinatorial species that decompose into molecules indexed by the same…
We present a simple proof of the factorization of (complex) symmetric matrices into a product of a square matrix and its transpose, and discuss its application in establishing a uniqueness property of certain antilinear operators.
Kronecker coefficients encode the tensor products of complex irreducible representations of symmetric groups. Their stability properties have been considered recently by several authors (Vallejo, Pak and Panova, Stembridge). We describe a…
We give a geometric method for determining the cohomology groups of a polyhedral product under suitable freeness conditions or with coefficients taken in a field. This is done by considering first the special case for which the pairs of…
We relate the $m$-truncated Kronecker products of symmetric functions to the semi-invariant rings of a family of quiver representations. We find cluster algebra structures for these semi-invariant rings when $m=2$. Each {\sf g}-vector cone…
This is a note for constructing fundamental invariants and computing the Hilbert series of the invariant subalgebras of tensor products of polynomial rings under the action by a direct product of symmetric groups. Our computation relies on…
A nonstandard application of bivariate polynomial interpolation is discussed: the implicitization of a rational algebraic curve given by its parametric equations. Three different approaches using the same interpolation space are considered,…
We prove an explicit formula for the tensor product with itself of an irreducible complex representation of the symmetric group defined by a rectangle of height two. We also describe part of the decomposition for the tensor product of…
Decay patterns of matrix inverses have recently attracted considerable interest, due to their relevance in numerical analysis, and in applications requiring matrix function approximations. In this paper we analyze the decay pattern of the…