Journal ArticleDOI
A Formula for the Exponential of a Real Skew-Symmetric Matrix of Order 4
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In this paper, the exponential matrix eA when A is a kew-symmetric real matrix of order 4 is derived, which is a generalization of the well known Rodrigues formula for skew symmetric matrices of order 3.Abstract:
In this short paper the formula of the exponential matrix e
A when A is a kew-symmetric real matrix of order 4 is derived. The formula is a generalization of the well known Rodrigues formula for skew-symmetric matrices of order 3.read more
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Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory
TL;DR: This book brings together a vast body of results on matrix theory for easy reference and immediate application with hundreds of identities, inequalities, and matrix facts stated rigorously and clearly.
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New Langevin and gradient thermostats for rigid body dynamics
TL;DR: In this article, two new thermostats, one of Langevin type and one of gradient (Brownian) type, for rigid body dynamics were introduced, which preserve the unit length of quaternions, without the need of a projection onto the unit sphere.
Journal ArticleDOI
Computation of the Exponential of Large Sparse Skew-Symmetric Matrices
TL;DR: The proposed method is based on two main steps: A is factorized into its tridiagonal form H by the well-known Lanczos iterative process, and then exp(A) is derived making use of an effective Schur decomposition of H.
Journal ArticleDOI
On the Rotation Matrix in Minkowski Space-Time
Mustafa Özdemir,Melek Erdoğdu +1 more
TL;DR: In this article, a Rodrigues-like formula is derived for 4 × 4 semi skew-symmetric real matrices in the Lorentzian rotation matrix R such that R = eA.
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An Alternative Approach to Elliptical Motion
TL;DR: In this paper, the authors examined the generation of elliptical rotations and to interpret the motion of a point on an ellipsoid using elliptic inner product and elliptic vector product.
References
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Book
Topics in Matrix Analysis
TL;DR: The field of values as discussed by the authors is a generalization of the field of value of matrices and functions, and it includes singular value inequalities, matrix equations and Kronecker products, and Hadamard products.
Journal ArticleDOI
Nineteen Dubious Ways to Compute the Exponential of a Matrix
Cleve B. Moler,Charles Van Loan +1 more
TL;DR: In this article, the exponential of a matrix could be computed in many ways, including approximation theory, differential equations, the matrix eigenvalues, and the matrix characteristic polynomial.
Journal ArticleDOI
Lie-Butcher theory for Runge-Kutta methods
TL;DR: In this article, it is shown that there is an intimate connection between Lie series and Lie groups on one hand and Butcher's celebrated theory of order conditions on the other, which leads to a theory for the order conditions, which can be developed in a completely coordinate free manner.
Journal ArticleDOI
Approximating the exponential from a Lie algebra to a Lie group
TL;DR: Some ideas based on the use of the Strang splitting for the approximation of matrix exponentials are presented, in tandem with general theory.
Journal ArticleDOI
Methods for the approximation of the matrix exponential in a Lie‐algebraic setting
Elena Celledoni,Arieh Iserles +1 more
TL;DR: In this paper, the authors studied the approximation of the matrix exponential in a particular context: given a Lie group G and its Lie algebra g, they sought approximants F(tB) of exp(tb) such that F(b) ∈ G if B ∈ g. They studied order conditions and implementation details and conclude the paper with some numerical experiments.
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