Related papers: U-cross Gram matrices and their invertibility

In this note, we summarize known results and open questions on the existence of isometric embeddings between different Schatten classes as well as obtain a new non-embeddability result using a novel method. We also provide a brief overview…

This paper introduces new classes of generalized inverses for square matrices named GD1, and the dual, called 1GD inverse. In addition, we discuss a few characterizations and representations of these inverses. The explicit expressions of…

We present an alternative proof of the result by P. Gerard and S. Grellier, stating that given two real sequences $(\lambda_n)_{n=1}^\infty$, $(\mu_n)_{n=1}^\infty$ satisfying the intertwining relations \[ |\lambda_1| > |\mu_1| >…

We derive a Matern Gaussian process (GP) on the vertices of a hypergraph. This enables estimation of regression models of observed or latent values associated with the vertices, in which the correlation and uncertainty estimates are…

We discuss the boundedness, Schatten-class properties and scattering theory of Helson matrices. We also discuss a class of Helson matrices induced by positive and signed measures. All the results of this paper are illustrated with several…

In this paper, we introduce two new forms of the dual Hartwig-Spindelb{\"o}ck decomposition and employ them to derive explicit representations for several classes of dual generalized inverses. Building on these representations, we further…

We establish Lipschitz stability properties for a class of inverse problems. In that class, the associated direct problem is formulated by an integral operator Am depending non-linearly on a parameter m and operating on a function u. In the…

We present a theoretically grounded Gaussian process framework that leverages neural feature maps to construct expressive kernels. We show that the learned feature map can be interpreted as an optimal low-rank approximation to a Gram matrix…

Binary Parseval frames share many structural properties with real and complex ones. On the other hand, there are subtle differences, for example that the Gramian of a binary Parseval frame is characterized as a symmetric idempotent whose…

We study the diagonalizability of the Atkin $U$-operator acting on Drinfeld cusp forms for $\Gamma_1(t)$ and $\Gamma(t)$ using Teitelbaum's interpretation as harmonic cocycles. We prove $U$ is diagonalizable for small weights and explicitly…

For a discrete group $\Gamma$ satisfying some finiteness conditions we give a Bredon projective resolution of the trivial module in terms of projective covers of the chain complex associated to certain posets of subgroups. We use this to…

In this paper, we prove the existence of a particular diagonalization for normal bounded operators defined on subspaces of $L^2(\mathfrak{S})$ where $\mathfrak{S}$ is a second countable LCA group. The subspaces where the operators act are…

We consider the algebra of invariants of $d$-tuples of $n\times n$ matrices under the action of the orthogonal group by simultaneous conjugation over an infinite field of characteristic $p$ different from two. It is well-known that this…

In digital signal processing, shift-invariant filters can be represented as a polynomial expansion of a shift operation,that is, the Z-transform representation. When extended to graph signal processing (GSP), this would mean that a…

In this paper, we introduce new representation and characterization of the weighted core inverse of matrices. Several properties of these inverses and their interconnections with other generalized inverses are also explored. Through…

Let X be a non-empty finite set, E be a finite dimensional euclidean vector space and G a finite subgroup of O(E), the orthognal group of E. Suppose GG={U_i | i in X} is a finite set of linear lines in E and an orbit of G on which its…

A binary tensor consists of $2^n$ entries arranged into hypercube format $2 \times 2 \times \cdots \times 2$. There are $n$ ways to flatten such a tensor into a matrix of size $2 \times 2^{n-1}$. For each flattening, $M$, we take the…

In this paper we extend the results in [Ra] on the representation of the Hecke algebra, determined by the matrix coefficients of a projective, unitary representation, in the discrete series of representations of the ambient group, to a more…

The well-known Asplund theorem states that the inverse of a (possibly one-sided) band matrix $A$ is a Green matrix. In accordance with quasiseparable theory, such a matrix admits a quasiseparable representation in its rank-structured part.…

Miniversal deformations for pairs of skew-symmetric matrices under congruence are constructed. To be precise, for each such a pair $(A,B)$ we provide a normal form with a minimal number of independent parameters to which all pairs of…