Exercises

These are exercises accompanying the book Projective Geometric Algebra Illuminated.

Exercises for Chapter 2

1. Show that Equation (2.35) properly constructs a line containing two points $$\mathbf p$$ and $$\mathbf q$$ with non-unit weights by considering $$\mathbf p / p_w \wedge \mathbf q / q_w$$ and then scaling by $$p_wq_w$$.

2. Let $$\mathbf u$$ be a basis element of the 4D projective algebra. Prove that if $$\mathbf u \wedge \overline{\mathbf u} = {\large\unicode{x1D7D9}}$$ and $$\underline{\mathbf u} \wedge \mathbf u = {\large\unicode{x1D7D9}}$$, then it must also be true that $$\mathbf u \vee \overline{\mathbf u} = \mathbf 1$$ and $$\underline{\mathbf u} \vee \mathbf u = \mathbf 1$$. That is, show that right and left complements under the wedge product are also the right and left complements under the antiwedge product.