从向量到几何代数
From Vectors to Geometric Algebra
摘要：
几何代数是向量概念和向量的向量的加法的自然产物。在回顾向量的加法的性质之后，引入了向量乘法，它编码了著名的勾股定理。欧几里得几何中定理的综合证明可以被强大的代数证明所取代。虽然我们在很大程度上限制我们的注意力在2和3维，几何代数是适用于任何数量的层面，并在欧几里德和非欧几里德几何。
英文摘要：
Geometric algebra is the natural outgrowth of the concept of a vector and the addition of vectors. After reviewing the properties of the addition of vectors, a multiplication of vectors is introduced in such a way that it encodes the famous Pythagorean theorem. Synthetic proofs of theorems in Euclidean geometry can then be replaced by powerful algebraic proofs. Whereas we largely limit our attention to 2 and 3 dimensions, geometric algebra is applicable in any number of dimensions, and in both Euclidean and non-Euclidean geometries.
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。
