Antiscalar

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An antiscalar in a geometric algebra is an element having antigrade 0. Antiscalars are multiples of the volume element given by the wedge product of all basis vectors.

The basis element representing the unit antiscalar is denoted by $$\large\unicode{x1D7D9}$$, a double-struck number one. The unit antiscalar $$\large\unicode{x1D7D9}$$ is the multiplicative identity of the geometric antiproduct.

For a general element $$\mathbf a$$, the notation $$a_{\large\unicode{x1D7D9}}$$ means the antiscalar component of $$\mathbf a$$.

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