Related papers: New permanent approximation inequalities via ident…

We study sample covariance matrices arising from rectangular random matrices with i.i.d. columns. It was previously known that the resolvent of these matrices admits a deterministic equivalent when the spectral parameter stays bounded away…

A new error bound for the linear complementarity problem is given when the involved matrix is a B-matrix. It is shown that this bound is sharper than some previous bounds [C.Q. Li, Y.T. Li. Note on error bounds for linear complementarity…

Let A and B be finite dimensional simple real algebras with division gradings by an abelian group G. In this paper we give necessary and sufficient conditions for the coincidence of the graded identities of A and B. We also prove that every…

We establish new explicit connections between classical (scalar) and matrix Gegenbauer polynomials, which result in new symmetries of the latter and further give access to several properties that have been out of reach before: generating…

An identity that is reminiscent of the Littlewood identity plays a fundamental role in recent proofs of the facts that alternating sign triangles are equinumerous with totally symmetric self-complementary plane partitions and that…

In this paper, we investigate a novel form of approximate orthogonality that is based on integral orthogonality. Additionally, we establish the fundamental properties of this new approximate orthogonality and examine its capability to…

We show that the apolar ideal to the determinant of a generic symmetric matrix is generated in degree two, and the apolar ideal to the permanent of a generic symmetric matrix is generated in degrees two and three. In each case we specify…

A remarkable property of Hermitian ensembles is their universal behavior, that is, once properly rescaled the eigenvalue statistics does not depend on particularities of the ensemble. Recently, normal matrix ensembles have attracted…

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…

The purpose of this paper is twofold. Firstly, the new matrix domains are constructed with the new infinite matrices and some properties are investigated. Furthermore, dual spaces of new matrix domains are computed and matrix…

Recently, metric learning and similarity learning have attracted a large amount of interest. Many models and optimisation algorithms have been proposed. However, there is relatively little work on the generalization analysis of such…

We introduce a remarkable new family of norms on the space of $n \times n$ complex matrices. These norms arise from the combinatorial properties of symmetric functions, and their construction and validation involve probability theory,…

We show that the conditions imposed on a second order linear differential equation with rational coefficients on the complex line by requiring it to have regular singularities with fixed exponents at the points of a finite set $P$ and…

Integral functionals based on convex normal integrands are minimized subject to finitely many moment constraints. The integrands are finite on the positive and infinite on the negative numbers, strictly convex but not necessarily…

A new approximation of the discriminant of a second order periodic differential equation is presented as a recursive summation of the evaluation of its excitation function at different values of time. The new approximation is obtained, at…

We consider pairs of a non-empty compact connected and locally connected Hausdorff space and a real-valued continuous function. Our aim is to measure the difference between this kind of the pairs. In this notes we introduce new…

We study the multifractal analysis of self-similar measures arising from random homogeneous iterated function systems. Under the assumption of the uniform strong separation condition, we see that this analysis parallels that of the…

Learning disentangled representations of textual data is essential for many natural language tasks such as fair classification, style transfer and sentence generation, among others. The existent dominant approaches in the context of text…

We relate a previous result of ours on families of Diophantine equations having only trivial solutions with a result on the approximation of an algebraic number by products of rational numbers and units. We compare this approximation with a…

Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…