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- 19:10, 12 May 2024 Errata (hist | edit) [958 bytes] Eric Lengyel (talk | contribs) (Created page with "This is the errata page for the ''Projective Geometric Algebra Illuminated''. To find out which printing you have, look on the copyright page. == First Printing == * '''Page 84.''' In Table 2.16, both bulk duals of $$\mathbf e_4$$ should be 0. * '''Page 156.''' The number of multiply-adds required for transforming a line with a motor did not include the work needed to calculate $$\mathbf a$$, $$\mathbf b$$, and $$\mathbf c$$. Each cross product adds 6 multiply-adds, s...")
- 01:48, 29 April 2024 Exercises (hist | edit) [3,315 bytes] Eric Lengyel (talk | contribs) (Created page with "These are exercises accompanying the book [https://www.amazon.com/dp/B0CXY8C72T/?tag=terathon-20 ''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 alg...")
- 21:27, 21 April 2024 Euclidean angle (hist | edit) [3,083 bytes] Eric Lengyel (talk | contribs) (Created page with "The cosine of the Euclidean angle $$\cos \phi(\mathbf a, \mathbf b)$$ between two geometric objects '''a''' and '''b''' can be measured by the homogeneous magnitude given by :$$\cos \phi(\mathbf a, \mathbf b) = \left\Vert \mathbf a \vee \mathbf b^\unicode["segoe ui symbol"]{x2606}\right\Vert_\unicode{x25CF} + \left\Vert\mathbf a \right\Vert_\unicode{x25CB}\left\Vert\mathbf b \right\Vert_\unicode{x25CB}$$. In the case that the grades of $$\mathbf a$$ and $$\mathbf b...")
- 01:48, 13 April 2024 Metrics (hist | edit) [1,252 bytes] Eric Lengyel (talk | contribs) (Created page with "The ''metric'' used in the 4D rigid geometric algebra over 3D Euclidean space is the $$4 \times 4$$ matrix $$\mathfrak g$$ given by :$$\mathfrak g = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 \\\end{bmatrix}$$ . The ''metric exomorphism matrix'' $$\mathbf G$$, often just called the "metric" itself, corresponding to the metric $$\mathfrak g$$ is the $$16 \times 16$$ matrix shown below. 420px The ''metri...")
- 06:15, 12 April 2024 Duals (hist | edit) [3,110 bytes] Eric Lengyel (talk | contribs) (Created page with "The ''metric dual'' or just "dual" of an object $$\mathbf u$$ is denoted by $$\mathbf u^\unicode["segoe ui symbol"]{x2605}$$ and defined as :$$\mathbf u^\unicode["segoe ui symbol"]{x2605} = \overline{\mathbf{Gu}}$$ , where $$\mathbf G$$ is the extended metric tensor. The ''metric antidual'' or just "antidual" of an object $$\mathbf u$$ is denoted by $$\mathbf u^\unicode["segoe ui symbol"]{x2606}$$ and defined as :$$\mathbf u^\unicode["segoe ui symbol"]{x2606} = \over...")
- 07:57, 22 January 2024 Weight contraction (hist | edit) [34 bytes] Eric Lengyel (talk | contribs) (Created page with "#REDIRECTION Interior products")
- 07:57, 22 January 2024 Bulk contraction (hist | edit) [34 bytes] Eric Lengyel (talk | contribs) (Created page with "#REDIRECTION Interior products")
- 07:57, 22 January 2024 Bulk expansion (hist | edit) [34 bytes] Eric Lengyel (talk | contribs) (Created page with "#REDIRECTION Interior products")
- 07:57, 22 January 2024 Weight expansion (hist | edit) [34 bytes] Eric Lengyel (talk | contribs) (Created page with "#REDIRECTION Interior products")
