Eric Lengyel: Created page with "A ''scalar'' in a geometric algebra is an element having grade 0. Scalars are just ordinary real numbers, and they do not involve any basis vectors. The basis element representing the unit scalar is denoted by $$\mathbf 1$$, a boldface number one. The unit scalar $$\mathbf 1$$ is the multiplicative identity of the geometric product. For a general element $$\mathbf a$$, the notation $$a_{\mathbf 1}$$ means the scalar component of $$\mathbf a$$. An ''antiscalar'..."

2023-07-15T06:20:18Z

Created page with "A ''scalar'' in a geometric algebra is an element having grade 0. Scalars are just ordinary real numbers, and they do not involve any basis vectors. The basis element representing the unit scalar is denoted by $$\mathbf 1$$, a boldface number one. The unit scalar $$\mathbf 1$$ is the multiplicative identity of the geometric product. For a general element $$\mathbf a$$, the notation $$a_{\mathbf 1}$$ means the scalar component of $$\mathbf a$$. An ''antiscalar'..."

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A ''scalar'' in a geometric algebra is an element having [[grade]] 0. Scalars are just ordinary real numbers, and they do not involve any basis vectors.

The basis element representing the unit scalar is denoted by $$\mathbf 1$$, a boldface number one. The unit scalar $$\mathbf 1$$ is the multiplicative identity of the [[geometric product]].

For a general element $$\mathbf a$$, the notation $$a_{\mathbf 1}$$ means the scalar component of $$\mathbf a$$.

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 $$\mathbf a$$.

== See Also ==

* [[Duality]]

Scalars and antiscalars - Revision history