Related papers: Metric Matrix in Barycentric Coordinates
A novel approach for solving linear estimation problem in multi-user massive MIMO systems is proposed. In this approach, the difficulty of matrix inversion is attributed to the incomplete definition of the dot product. The general…
A generalized definition of the determinant of matrices is given, which is compatible with the usual determinant for square matrices and keeps many important properties, such as being an alternating multilinear function, keeping…
Metrics on the space of sets of trajectories are important for scientists in the field of computer vision, machine learning, robotics, and general artificial intelligence. However, existing notions of closeness between sets of trajectories…
Tropical mathematics is used to establish a correspondence between certain microscopic and macroscopic objects in statistical models. Tropical algebra gives a common framework for macrosystems (subsets) and their elementary constituents…
We study inequalities between the hyperbolic metric and intrinsic metrics in convex polygonal domains in the complex plane. Special attention is paid to the triangular ratio metric in rectangles. A local study leads to an investigation of…
Metric embedding has become a common technique in the design of algorithms. Its applicability is often dependent on how high the embedding's distortion is. For example, embedding finite metric space into trees may require linear distortion…
The existence of kinematic formulas for area measures with respect to any connected, closed subgroup of the orthogonal group acting transitively on the unit sphere is established. In particular, the kinematic operator for area measures is…
The aim of this paper is to derive explicit formulae for the Riemannian Bures metric on the manifold of (finite dimensional) nondegenerate density matrices. The computation of the Bures metric using the presented equations does not require…
We investigate and discuss when the inverse of a multivariate truncated moment matrix of a measure $\mu$ has zeros in some prescribed entries. We describe precisely which pattern of these zeroes corresponds to independence, namely, the…
Barycentric coordinates are frequently used as interpolants to shade computer graphics images. A simple equation transforms barycentric coordinates from screen space into eye space in order to undo the perspective transformation and permit…
In many classification tasks, the set of target classes can be organized into a hierarchy. This structure induces a semantic distance between classes, and can be summarised under the form of a cost matrix, which defines a finite metric on…
Compact metric spaces form an important class of metric spaces, but the category that they define lacks many important properties such as completeness and cocompleteness. In recent studies of "metric domain theory" and Stone-type dualities,…
We propose and investigate a bi-infinite matrix approach to the multiplication and composition of formal Laurent series. We generalize the concept of Riordan matrix to this bi-infinite context, obtaining matrices that are not necessarily…
In this paper, we review the problem of matrix completion and expose its intimate relations with algebraic geometry, combinatorics and graph theory. We present the first necessary and sufficient combinatorial conditions for matrices of…
In this paper we outline a Matrix Ansatz approach to some problems of combinatorial enumeration. The idea is that many interesting quantities can be expressed in terms of products of matrices, where the matrices obey certain relations. We…
This paper is to build a primitive framework for a new possible extended system of real mathematical analysis - the Isomorphic Mathematical Analysis System (IMAS). It is based on some new concepts: e.g. isomorphic frame,…
We discuss the general structure of metric geometries, and how metricity implies the complete antisymmetry of Cartan tensor; an application in the frame of Lie group theory is given. Interpretations of the completely antisymmetric torsion…
A physical metric is constructed as one that gives a coordinate independent result for the time delay in infinite order in the perturbation expansion in the gravitational constant. A compact form for the metric is obtained. One result is…
A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the…
The de Sitter manifold admits a wide variety of interesting coordinatizations. The 'atlas' is a compilation of the coordinate charts referenced throughout the literature, and is presented in the form of tables, the starting point being the…