发表机构
CINVESTAV-IPN（墨西哥国立理工学院高级研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种简化方法推导SO(3)下笛卡尔各向同性张量基，通过将各向同性条件转化为旋转矩阵的代数方程组建立低秩基，给出高阶张量数量的组合解释，并倡导用Gram矩阵法解决线性相关性问题。
AI 中文摘要
本文提出了一种用于推导特殊正交群SO(3)下笛卡尔各向同性张量基的替代简化方法。通过将各向同性条件的传统解释转换为直接分析旋转矩阵本身的代数方程组（而非张量分量），仅用几行即可明确建立低秩基，无需有限坐标旋转或无穷小生成元的复杂缩并。此外，对一般高阶张成集中的张量数量给出了清晰的组合解释，最后倡导采用Gram矩阵法作为高效计算筛选工具，以解决后续的线性相关性问题。
英文摘要
An alternative, streamlined methodology is presented for deriving the isotropic Cartesian tensor bases under the special orthogonal group $\text{SO}(3)$. By shifting the traditional interpretation of the isotropy condition to analyze it as an algebraic system of equations for the rotation matrices themselves rather than the tensor components, lower-rank bases can be explicitly established in just a few lines without requiring finite coordinate rotations or complicated contractions of infinitesimal generators. Furthermore, a transparent combinatorial interpretation is provided for the number of tensors in the general higher-rank spanning sets. Finally, the Gram-matrix method is advocated as an efficient computational sieve to resolve the subsequent linear dependence.
Comments5 pages
