Metrics

The metric used in the 5D projective geometric algebra over 4D spacetime is the $$5 \times 5$$ matrix $$\mathfrak g$$ given by

$$\mathfrak g = \begin{bmatrix} -1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 \\\end{bmatrix}$$ .

The metric exomorphism matrix $$\mathbf G$$, often just called the "metric" itself, corresponding to the metric $$\mathfrak g$$ is the $$32 \times 32$$ matrix shown below.

The metric antiexomorphism matrix $$\mathbb G$$, often called the "antimetric", corresponding to the metric $$\mathfrak g$$ is the $$32 \times 32$$ matrix shown below.

See Also

• Duals
• Dot products