微分学、张量积与记法的重要性
Differential Calculus, Tensor Products and the Importance of Notation
摘要：
一个有效的坐标自由符号阐明区分矩阵表达式和其他功能之间的高维向量空间。这种微分方法是已知的，但在文献中没有很好地解释。在课程的早期教授它可以避免单调的元素微分，并为理解微积分的更高级应用提供更好的基础。此外，它自然导致张量积，一个主题以前被认为太难，以基本的方式迅速激励。
英文摘要：
An efficient coordinate-free notation is elucidated for differentiating matrix expressions and other functions between higher-dimensional vector spaces. This method of differentiation is known, but not explained well, in the literature. Teaching it early in the curriculum would avoid the tedium of element-wise differentiation and provide a better footing for understanding more advanced applications of calculus. Additionally, it is shown to lead naturally to tensor products, a topic previously considered too difficult to motivate quickly in elementary ways.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
