テンソル記法による行列リー群演算の表現改善
Improved Representation of Matrix Lie Group Operations through Tensor Notation
行列リー群の演算をテンソルとアインシュタイン記法で表現する新しい数学的ツールを提案し、推定問題における微分や操作の明確化を図った論文。
著者: Clark Taylor
分類: cs.RO, cs.NA, math.NA
原文アブストラクト
Several recent papers have demonstrated the utility of using Lie groups within estimation problems, yielding improved accuracy and consistency. This paper introduces a new tool for describing operations with matrix Lie groups: tensors and the Einstein summation notation. While tensors and Einstein notation are well-known in other research fields, applying this mathematical notation to represent and compute matrix Lie derivatives is novel. More importantly, this new notation greatly clarifies the derivatives and operations necessary to work with matrix Lie Groups in (gradient-based) estimation frameworks. Therefore, the main contribution of this paper is not a new capability, but a more perspicuous mathematical notation for working with matrix Lie groups.