🎬how a completely anti-symmetric tensor is constructed from a tensor density
The covariant and contravariant forms of a completely anti-symmetric tensor have an inverse relationship determined by the geometry of the coordinate system. The demo visually proves this by showing that as the off-diagonal component of the metric tensor changes, the covariant component decreases while the contravariant component increases. This confirms that multiplying by (for the covariant form) and by (for the contravariant form) correctly scales the tensor to match the underlying geometry.
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