Related papers: Matrix differentiation with diagrammatic notation
We describe efficient differentiation methods for computing Jacobians and gradients of a large class of matrix functions including the matrix logarithm $\log(A)$ and $p$-th roots $A^{\frac{1}{p}}$. We exploit contour integrals and conformal…
The solution of systems of non-autonomous linear ordinary differential equations is crucial in a variety of applications, such us nuclear magnetic resonance spectroscopy. A new method with spectral accuracy has been recently introduced in…
We discuss some problems with the indefinite integral notation and the way of teaching of integrals in Calculus. Based on the discussion, and in order to avoid mistakes, we propose another notation for indefinite integrals.
A matrix-compression algorithm is derived from a novel isogenic block decomposition for square matrices. The resulting compression and inflation operations possess strong functorial and spectral-permanence properties. The basic observation…
This short article contains the construction of a construction that generalizes the concept of the derivative of a function of one variable, using the theory of filters. The paper presents a new concept, demonstrates that it really…
Matrix norms can be used to measure the "distance" between two matrices which translates naturally to the problem of calculating the unitary deviation of the neutrino mixing matrices. Variety of matrix norms opens a possibility to measure…
In this paper, we propose an online algorithm to compute matrix factorizations. Proposed algorithm updates the dictionary matrix and associated coefficients using a single observation at each time. The algorithm performs low-rank updates to…
This paper proposes a novel matrix rank-one decomposition for quaternion Hermitian matrices, which admits a stronger property than the previous results in (sturm2003cones,huang2007complex,ai2011new). The enhanced property can be used to…
I consider differential of mapping $f$ of continuous division ring as linear mapping the most close to mapping $f$. Different expressions which correspond to known deffinition of derivative are supplementary. I explore the Gateaux…
In this article, we show multiple inequalities for the singular values of the difference of matrix means. The obtained results refine and complement some well established results in the literature. Although we target singular values…
The proper handling of 3D orientations is a central element in many optimization problems in engineering. Unfortunately many researchers and engineers struggle with the formulation of such problems and often fall back to suboptimal…
The confusion matrix, a ubiquitous visualization for helping people evaluate machine learning models, is a tabular layout that compares predicted class labels against actual class labels over all data instances. We conduct formative…
The problem of matrix factorization motivated by diffraction or elasticity is studied. A powerful tool for analyzing its solutions is introduced, namely analytical continuation formulae are derived. Necessary condition for commutative…
In this paper, a novel approach for coding nominal data is proposed. For the given nominal data, a rank in a form of complex number is assigned. The proposed method does not lose any information about the attribute and brings other…
We develop a rewriting theory suitable for diagrammatic algebras and lay down the foundations of a systematic study of their higher structures. In this paper, we focus on the question of finding bases. As an application, we give the first…
The capability of discretization of matrix elements in the problem of quadratic functional minimization with linear member built on matrix in N-dimensional configuration space with discrete coordinates is researched. It is shown, that…
In this paper, we introduce the new construction of fractional derivatives and integrals with respect to a function, based on a matrix approach. We believe that this is a powerful tool in both analytical and numerical calculations. We begin…
We propose a method for characterizing large complex networks by introducing a new matrix structure, unique for a given network, which encodes structural information; provides useful visualization, even for very large networks; and allows…
For quantum systems described by finite matrices, linear and affine maps of matrices are shown to provide equivalent descriptions of evolution of density matrices for a subsystem caused by unitary Hamiltonian evolution in a larger system;…
This note presents several conditions to characterize real matrix similarity between a Hurwitz matrix (and then more generally, a real square matrix) and a diagonal dominant matrix.