2.5 Conventions | Geometric Algebra for Physicists

Transcript

welcome to section 2.5 on conventions of geometric algebra there are many conventions which help simplify expressions within geometric algebra and we will go over some of them first off there's an order of operations that allows us to simplify by not having to use brackets or parentheses the inner product be comes before the outer product which comes before the geometric product thus the below equation is true there's also something that is known as reversion which is switching the order of vectors within any product we denote it with the dagger or with the tilde therefore we can see that bi vectors and tri vectors change sign and we can decompose a general multi-vector within g sub 3 as follows and a multi-vector is homogeneous if and only if it contains terms of a single grade yeah thank you for watching this short lesson i did say it would be short in the last episode and next section will be on 2.6 which is reflections