File:Antimetric-rga-3d.svg and Metrics: Difference between pages
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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...") |
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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. | |||
[[Image:metric-rga-3d.svg|420px]] | |||
The ''metric antiexomorphism matrix'' $$\mathbb G$$, often called the "antimetric", corresponding to the metric $$\mathfrak g$$ is the $$16 \times 16$$ matrix shown below. | |||
[[Image:antimetric-rga-3d.svg|420px]] |
Revision as of 01:48, 13 April 2024
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.
The metric antiexomorphism matrix $$\mathbb G$$, often called the "antimetric", corresponding to the metric $$\mathfrak g$$ is the $$16 \times 16$$ matrix shown below.
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