Metrics

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.