Abstract Infinite Leslie matrices are studied. The purely linear algebraic concept of weighed kneading determinant is introduced to solve linear difference equations associated with Leslie matrices. The method applies both to finite and infinite matrices. In the finite case this technique simplifies the computations. The asymptotic properties of the solutions are established using the positive ...

In this paper, real matrix representations of split quaternions are examined in terms of the casual character of quaternion. Then, we give De-Moivre’ s formula for real matrices of timelike and spacelike split quaternions, separately. Finally, we state the Euler theorem for real matrices of pure split quaternions.

Ai = Prismatic joints along the horizontal circular guide Bi = Spherical joints on the moving platform Ci = Prismatic joints on the vertical columns (i = 1,2,3) {F} = Fixed global reference frame {M} = Moving frame α, β, γ = ZYX Euler angles of rotation about the three joint axes of rider. α', β', γ', δ' = ZYXZ’ Euler angles of rotation about the four joint axes of chair on the moving platform ...

In a previous paper [1] an Euler angle parameterization for SU (N) was given. Here we present a generalized Euler angle parameterization for U (N). The formula for the calculation of the volume for U (N), CP N as well as other SU (N) and U (N) cosets, normalized to this parameterization, will also be given. In addition, the mixed and pure state product measures for N-dimensional density matrice...

This paper is concerned with the generalized Euler polynomial matrix $\E^{(\alpha)}(x)$ and $\E$. Taking into account some properties of polynomials numbers, we deduce product formulae for determine inverse We establish explicit expressions $\E(x)$, which involving Pascal, Fibonacci Lucas matrices, respectively. From these get new interesting identities numbers. Also, provide factorizations in ...

Three and four parameter representations of 3x3 orthogonal matrices are extended to the general case of proper NxN orthogonal matrices. These developments generalize the classical Rodrigues parameter, the Euler parameters, and the recently introduced modified Rodrigues parameters to higher dimensions. The developments presented generalize and extend the classical result known as the Cayley tran...

We analyze the correspondence between finite sequences of finitely supported probability distributions and finite-dimensional, real, symmetric, tridiagonal matrices. In particular, we give an intrinsic description of the topology induced on sequences of distributions by the usual Euclidean structure on matrices. Our results provide an analytical tool with which to study ensembles of tridiagonal...

We show that the Akiyama-Tanigawa algorithm and Chen’s variant for computing Bernoulli numbers can be generalized to Carlitz’s q-Bernoulli numbers. We also put these algorithms in the larger context of generalized Euler-Seidel matrices.

We investigate the limit behaviour of the spectral measures of matrices following the Gibbs measure for the Ising model on random graphs, Potts model on random graphs, matrices coupled in a chain model or induced QCD model. For most of these models, we prove that the spectral measures converge almost surely and describe their limit via solutions to an Euler equation for isentropic flow with neg...