> Geometric algebra is to exterior algebra as inner product spaces are to vector spaces To get from x∧x to |x|², you need a norm. And I guess linearity must b

> Geometric algebra is to exterior algebra as inner product spaces are to vector spaces To get from x∧x to |x|², you need a norm. And I guess linearity must break down somewhere unless that norm is compatible with an inner product. Thanks, I missed that point. > But I guess the intent is clear enough. Once you have u and b, you can define a = u - b.