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- 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$$ matrix shown below. 420px The ''metri...")
- 06:15, 12 April 2024 Duals (hist | edit) [2,908 bytes] Eric Lengyel (talk | contribs) (Created page with "The ''metric dual'' or just "dual" of an object $$\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")