Related papers: Time Derivative of Rotation Matrices: A Tutorial
This tutorial, addressing physics teachers and undergraduate students, aims at clarifying some aspects of time in special relativity. In particular, time dilation is usually presented only as the well-known ratio of lab time over proper…
There have been several algorithms designed to optimise matrix multiplication. From schoolbook method with complexity $O(n^3)$ to advanced tensor-based tools with time complexity $O(n^{2.3728639})$ (lowest possible bound achieved), a lot of…
DTW calculates the similarity or alignment between two signals, subject to temporal warping. However, its computational complexity grows exponentially with the number of time-series. Although there have been algorithms developed that are…
We consider estimation of covariance matrices and their inverses (a.k.a. precision matrices) for high-dimensional stationary and locally stationary time series. In the latter case the covariance matrices evolve smoothly in time, thus…
A method is proposed to reconstruct a cyclic time-inhomogeneous Markov pro- cess from measured data. First, a time-inhomogeneous Markov model is fit to the data, taken here from measurements on a wind turbine. From the time-dependent…
This note deals with a simultaneous approximation of several matrices by a finite family of diagonalizable matrices satisfying an additional condition for the spectrum of a matrix product. That is the simplicity of all eigenvalues.
There are many papers devoted to derivation of Lorentz Transformations (LT). Many people have pro posed alternative derivations. Their analysis allows looking at LT and their consequences from different standpoints. At the same time it is…
We show that two tensor permutation matrices permutate tensor product of rectangle matrices. Some examples, in the particular case of tensor commutation matrices, for studying some linear matrix equations are given.
A rotational lattice is a structure (L;\vee,\wedge, g) where L=(L;\vee,\wedge) is a lattice and g is a lattice automorphism of finite order. We describe the subdirectly irreducible distributive rotational lattices. Using J\'onsson's lemma,…
This paper presents a general form of the covariance matrix structure for a vector random field that is axially symmetric and mean square continuous on the sphere and provides a series representation for a longitudinally reversible one. The…
The well-known linear Doppler effect arises from the linear motion between source and observer, while the less well-known rotational Doppler effect arises from the rotational motion. Here, we present both theories and experiments…
The matrix differential equation $x'(t) = Q(t)x(t), x(0) = x_0$ is considered in the case where $Q(t)$ is an unspecified matrix function of time, with the only constraint that $Q(t)\in \mset$ for every $t$, where $\mset$ is a prescribed…
We consider spacetime to be a 4-dimensional differentiable manifold that can be split locally into time and space. No metric, no linear connection are assumed. Matter is described by classical fields/fluids. We distinguish electrically…
A matrix is totally positive if all of its minors are positive. This notion of positivity coincides with the type A version of Lusztig's more general total positivity in reductive real-split algebraic groups. Since skew-symmetric matrices…
In this paper, we consider mutations of skew-symmetrizable matrices of rank 3. Every skew-symmetrizable matrix corresponds to a weighted quiver, and we study the conditions when this quiver is always cyclic after applying mutations. In this…
A causal scattering matrix is constructed by means of the mixed chronological and normal product of the free quantum fields of different variables. This scattering matrix does not contain the diverging integrals.
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 give conditions on a matrix which guarantee that it is similar to a centrosymmetric matrix. We use this conditions to show that some $4 \times 4$ and $6 \times 6$ Toeplitz matrices are similar to centrosymmetric matrices.…
Dynamical processes can be classified in various ways as deterministic or stochastic, and continuous or discrete time. All these types can be studied by the path-spaces they generate, and stationary measures on that path-space. Such…
This text is a survey on symmetric matrices. It serves as a script for a module to be taught at university.