Related papers: A Generalized Matrix Inverse that is Consistent wi…

In this paper, we derive high-dimensional asymptotic properties of the Moore-Penrose inverse and, as a byproduct, of various ridge-type inverses of the sample covariance matrix. In particular, the analytical expressions of the asymptotic…

This paper pursues a twofold goal. First, we introduce and study in detail a new notion of variational analysis called generalized metric subregularity, which is a far-going extension of the conventional metric subregularity conditions. Our…

This paper analyzes the convergence of fixed-point iterations of the form u = f(u) and the properties of the inverse of the related pentadiagonal matrices, associated with the fourth-order nonlinear beam equation. This nonlinear problem is…

Generalized symmetries have emerged as a powerful organizing principle for exotic quantum phases. However, their role in open quantum systems, especially for non-invertible cases, remains largely unexplored. We address this by applying a…

This paper concerns the inverse problem of determining a planar conductivity inclusion. Our aim is to analytically recover from the generalized polarization tensors (GPTs), which can be obtained from exterior measurements, a homogeneous…

Gauge-invariant treatments of general-relativistic higher-order perturbations on generic background spacetime is proposed. We show the fact that the linear-order metric perturbation is decomposed into gauge-invariant and gauge-variant…

The connection between symmetries and linearizations of discrete-time dynamical systems is being inverstigated. It is shown, that existence of semigroup structures related to the vector field and having linear representations enables…

Standard convolutions are prevalent in image processing and deep learning, but their fixed kernels limits adaptability. Several deformation strategies of the reference kernel grid have been proposed. Yet, they lack a unified theoretical…

The centralizer algebra of a matrix consists of those matrices that commute with it. We investigate the basic representation-theoretic invariants of centralizer algebras, namely their radicals, projective indecomposable modules, injective…

Various characterizations are offered of injectivity of the canonical fundamental group homomorphism for a certain class of inverse limit spaces. One application characterizes the existence of a kind of generalized universal cover.

When an inverse problem is solved by a gradient-based optimization algorithm, the corresponding forward and adjoint problems, which are introduced to compute the gradient, can be also solved iteratively. The idea of iterating at the same…

Dirichlet integrals and the associated Dirichlet statistical densities are widely used in various areas. Generalizations of Dirichlet integrals and Dirichlet models to matrix-variate cases, when the matrices are real symmetric positive…

Matrix completion constantly receives tremendous attention from many research fields. It is commonly applied for recommender systems such as movie ratings, computer vision such as image reconstruction or completion, multi-task learning such…

Matroids generalize the familiar notion of linear dependence from linear algebra. Following a brief discussion of founding work in computability and matroids, we use the techniques of reverse mathematics to determine the logical strength of…

For a multivariate normal distribution, the sparsity of the covariance and precision matrices encodes complete information about independence and conditional independence properties. For general distributions, the covariance and precision…

We deal with germs of diffeomorphisms that are reversible under an involution. We establish that this condition implies that, in general, both the family of reversing symmetries and the group of symmetries are not finite, in contrast with…

The purpose of this paper is to analyze the Moore-Penrose pseudo-inversion of symmetric real matrices with application in the graph theory. We introduce a novel concept of positively and negatively pseudo-inverse matrices and graphs. We…

The Rytov approximation is known in near-infrared spectroscopy including diffuse optical tomography. In diffuse optical tomography, the Rytov approximation often gives better reconstructed images than the Born approximation. Although…

This paper studies the unitary diagonalization of matrices over formal power series rings. Our main result shows that a normal matrix is unitarily diagonalizable if and only if its minimal polynomial completely splits over the ring and the…

In this paper we derive a representation of an arbitrary real matrix M as the difference of a real matrix A and the transpose of its inverse. This expression may prove useful for progressing beyond known results for which the appearance of…