The Exponential of Skew-Symmetric Matrices
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The Exponential of Skew-Symmetric Matrices: A Nearby Inverse and Efficient Computation of Derivatives
arXiv:2506.18302v2 Announce Type: replace-cross Abstract: The matrix exponential restricted to skew-symmetric matrices has numerous applications, notably in view of its interpretation as the Lie group exponential and Riemannian exponential for the special orthogonal group. We characterize the invertibility of the derivative of the skew-restricted exponential, thereby providing a simple expression of the tangent conjugate locus of the orthogonal group. In view of the skew restriction, this...