What is the inverse of a vector?
The article begins:<p>&gt;In this post we will re-invent a form of math that is far superior to the one you learned in school. The ideas herein are nothing short of revolutionary.<p>and concludes:<p>&gt; I firmly believe that in 100 years, Geometric Algebra will be the dominant way of introducing students to mathematical physics. In the same way that Newton&#x27;s notation for Calculus is no longer the dominant one, or that Maxwell&#x27;s actual equations for Electromagnetism have been replaced by Heaviside&#x27;s, textbooks will change because a better system has come along.<p>These claims are wrong.<p>There are three standard notation methods in physics: vectors, tensors, and differential forms. Geometric algebra is, as the article points out, a more powerful version of the usual vector notation. But it is deficient in various ways when compared to tensor notation (for calculations) and differential forms (e.g. if you want to work basis-free). [I&#x27;m oversimplifying a bit, but a full discussion is too long for a comment here.]<p>Anyway, geometric algebra is not some esoteric secret. People know about it and have decided not to teach it, because the stuff that&#x27;s already taught is better.<p>[I picked up this specific phrasing from another user here, knzhou, which I think is a particularly good way of explaining it.]