In this paper, we consider the generalized degenerate Bernoulli/Euler polynomial matrices and study some algebraic properties for them. particular, focus our attention on matrix-inversion formulae involving these matrices. Furthermore, provide analytic so-called Pascal matrix of first kind, factorizations Euler matrix.

Gregory S. Chirikjian Johns Hopkins University 2.1 Rotations in Three Dimensions Rules for Composing Rotations • Euler Angles • The Matrix Exponential 2.2 Full Rigid-Body Motion Composition of Motions • Screw Motions 2.3 Homogeneous Transforms and the Denavit-Hartenberg Parameters Homogeneous Transformation Matrices • The Denavit-Hartenberg Parameters in Robotics 2.4 Infinitesimal Motions and A...

A multi-parameter family of optimal Euler preconditioners are explored. This uncovers the link between the various matrices derived by Van Leer et al. and Turkel, and also presents an attempt to derive more effective matrices. The preconditioning technique, which is based on a difference scheme rather than on partial differential equations, is extended from the Euler equations to the Navier-Sto...

This paper extends the singular value decomposition to a path of matrices E(t). An analytic singular value decomposition of a path of matrices E(t) is an analytic path of factorizations E(t) = X(t)S(t)Y (t)T where X(t) and Y (t) are orthogonal and S(t) is diagonal. To maintain di erentiability the diagonal entries of S(t) are allowed to be either positive or negative and to appear in any order....

This paper extends the singular value decomposition to a path of matrices E(t). An analytic singular value decomposition of a path of matrices E(t) is an analytic path of factorizations E(t) = X(t)S(t)Y (t)T where X(t) and Y (t) are orthogonal and S(t) is diagonal. To maintain di erentiability the diagonal entries of S(t) are allowed to be either positive or negative and to appear in any order....

This paper studies block matrices A = [Aij ] ∈ C, where every block Aij ∈ C for i, j ∈ 〈m〉 = {1, 2, . . . ,m} and Aii is non-Hermitian positive definite for all i ∈ 〈m〉. Such a matrix is called an extended H−matrix if its block comparison matrix is a generalized M−matrix. Matrices of this type are an extension of generalized M−matrices proposed by Elsner and Mehrmann [L. Elsner and V. Mehrmann....

This paper studies block matrices A = [Aij ] ∈ C, where every block Aij ∈ C for i, j ∈ 〈m〉 = {1, 2, . . . ,m} and Aii is non-Hermitian positive definite for all i ∈ 〈m〉. Such a matrix is called an extended H−matrix if its block comparison matrix is a generalized M−matrix. Matrices of this type are an extension of generalized M−matrices proposed by Elsner and Mehrmann [L. Elsner and V. Mehrmann....

Any rotation of a 3-dimensional object can be performed by three consecutive rotations over Euler angles. Intrinsic rotations produce the same result as extrinsic rotations in transformation. Euler rotations are the movement obtained by changing one of the Euler angles while leaving the other two constant. These Euler rotations are applied in a simple two-axis gimbals set mounted on an automoti...