In this post, Eric Lengyel discusses the misconceptions and errors in geometric algebra literature, focusing on inner products, contractions, and duals. He criticizes the lack of mathematical rigor in some definitions, arguing that many authors copy flawed ideas from others. Lengyel highlights the importance of establishing correct foundational concepts to prevent the need for inelegant workarounds later on. He provides alternative, clearer definitions for contraction and dual operations, showcasing a more straightforward approach to geometric algebra. By addressing these issues, he aims to improve the understanding and application of geometric algebra concepts, offering valuable insights into this field.
https://terathon.com/blog/poor-foundations-ga.html