Related papers: The geometric mean of two matrices from a computat…
It is well-understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs…
We propose a totally functional view of geometric matrix completion problem. Differently from existing work, we propose a novel regularization inspired from the functional map literature that is more interpretable and theoretically sound.…
The classical AM-GM inequality has been generalized in a number of ways. Generalizations which incorporate variance appear to be the most useful in economics and finance, as well as mathematically natural. Previous work leaves unanswered…
In this paper, we generalize the geometric mean of two positive definite matrices to that of third-order tensors using the notion of T-product. Specifically, we define the geometric mean of two T-positive definite tensors and verify several…
Some inequalities for positive linear maps on matrix algebras are given, especially asymmetric extensions of Kadison's inequality and several operator versions of Chebyshev's inequality. We also discuss well-known results around the matrix…
We address the general mathematical problem of computing the inverse $p$-th root of a given matrix in an efficient way. A new method to construct iteration functions that allow calculating arbitrary $p$-th roots and their inverses of…
This paper studies geometric properties of the Iterated Matrix Multiplication polynomial and the hypersurface that it defines. We focus on geometric aspects that may be relevant for complexity theory such as the symmetry group of the…
The concept of Loewner (partial) order for general complex matrices is introduced. After giving the definition of arithmetic, geometric, and harmonic mean for accretive-dissipative matrices, we study their basic properties. An AM-GM-HM…
We describe a simple geometric transformation of triangles which leads to an efficient and effective algorithm to smooth triangle and tetrahedral meshes. Our focus lies on the convergence properties of this algorithm: we prove the…
We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…
The geometric mean method (GMM) and the eigenvector method (EM) are well-known approaches to deriving information from pairwise comparison matrices in decision making processes. However, the original algorithms of these methods are…
We study the differential and metric structures of the set of real square roots of a non-singular real matrix, under the assumption that the matrix and its square roots are semi-simple, or symmetric, or orthogonal.
We consider the simplest gauge theories given by one- and two- matrix integrals and concentrate on their stringy and geometric properties. We remind general integrable structure behind the matrix integrals and turn to the geometric…
We present here necessary and sufficient conditions for the invertibility of circulant and symmetric matrices that depend on three parameters and moreover, we explicitly compute the inverse. The techniques we use are related with the…
In this paper, we analyze the process of "assembling" new matrix geometric means from existing ones, through function composition or limit processes. We show that for n=4 a new matrix mean exists which is simpler to compute than the…
A brief introduction to geometric valuation theory is given. The focus is on classification results for valuations on convex bodies and on function spaces.
Polynomial functions are a usual choice to model the nonlinearity of lenses. Typically, these models are obtained through physical analysis of the lens system or on purely empirical grounds. The aim of this work is to facilitate an…
This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…
Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations. In particular, a knowledge of the symmetries may help reduce the problem dimension, cut…
A mathematical model is a function taking certain arguments and returning a theoretical prediction of a feature of a physical system. The arguments to the mathematical model can be split into two groups; (a) controllable variables of the…