相关论文: Simple Spectral Bounds for Sums of Certain Kroneck…

Our main result is an elementary derivation of the spectral decomposition of hypermatrices generated by arbitrary combinations of Kronecker products and direct sums of cubic side length 2

Compound matrices play an important role in many fields of mathematics and have recently found new applications in systems and control theory. However, the explicit formulas for these compounds are non-trivial and not always easy to use.…

We investigate the iterated Kronecker product of a square matrix with itself and prove an invariance property for symmetric subspaces. This motivates the definition of an iterated symmetric Kronecker product and the derivation of an…

This note deals with a simultaneous approximation of several matrices by a finite family of diagonalizable matrices satisfying an additional condition for the spectrum of a matrix product. That is the simplicity of all eigenvalues.

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…

A novel tensor-based formula for solving the linear systems involving Kronecker sum is proposed. Such systems are directly related to the matrix and tensor forms of Sylvester equation. The new tensor-based formula demonstrates the…

We present decay bounds for a broad class of Hermitian matrix functions where the matrix argument is banded or a Kronecker sum of banded matrices. Besides being significantly tighter than previous estimates, the new bounds closely capture…

Kernel methods are successful approaches for different machine learning problems. This success is mainly rooted in using feature maps and kernel matrices. Some methods rely on the eigenvalues/eigenvectors of the kernel matrix, while for…

Combined perturbation bounds are presented for eigenvalues and eigenspaces of Hermitian matrices or singular values and singular subspaces of general matrices. The bounds are derived based on the smooth decompositions and elementary…

We describe the inequalities on the possible eigenvalues of products of unitary matrices in terms of quantum Schubert calculus. Related problems are the existence of flat connections on the punctured two-sphere with prescribed holonomies,…

We provide non-asymptotic, relative deviation bounds for the eigenvalues of empirical covariance and Gram matrices in general settings. Unlike typical uniform bounds, which may fail to capture the behavior of smaller eigenvalues, our…

We present a lower bound on the Kronecker coefficients for tensor squares of the symmetric group via the characters of~$S_n$, which we apply to obtain various explicit estimates. Notably, we extend Sylvester's unimodality of $q$-binomial…

This work is concerned with finite range bounds on the variance of individual eigenvalues of random covariance matrices, both in the bulk and at the edge of the spectrum. In a preceding paper, the author established analogous results for…

We show that the well known Kronecker product is a suitable tool for the construction of matrix representations of widely used spin Hamiltonians. In this way we avoid the explicit use of basis sets for the construction of the matrix…

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…

We derive inclusion regions for the eigenvalues of matrix polynomials expressed in a general polynomial basis, which can lead to significantly better results than traditional bounds. We present several applications to engineering problems.

The product of a Hermitian matrix and a positive semidefinite matrix has only real eigenvalues. We present bounds for sums of eigenvalues of such a product.

We present a new method for obtaining norm bounds for random matrices, where each entry is a low-degree polynomial in an underlying set of independent real-valued random variables. Such matrices arise in a variety of settings in the…

We consider a random process with discrete time formed by singular values of products of truncations of Haar distributed unitary matrices. We show that this process can be understood as a scaling limit of the Schur process, which gives…

We establish a new spectral inequality for the quantified estimation of the $H^s$-norm, $s\ge 0$ of a finite linear combination of eigenfunctions in a domain in terms of its $H^s$-norm in a strictly open subset of the whole domain. The…