Grade and antigrade - Revision history

Eric Lengyel at 23:31, 13 April 2024

2024-04-13T23:31:12Z

← Older revision		Revision as of 23:31, 13 April 2024
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	[[Scalars]] have grade 0, and [[antiscalars]] have grade ''n''. [[Vectors]] have grade 1, and [[antivectors]] have antigrade 1. [[Bivectors]] have grade 2, and [[trivectors]] have grade 3.		[[Scalars]] have grade 0, and [[antiscalars]] have grade ''n''. [[Vectors]] have grade 1, and [[antivectors]] have antigrade 1. [[Bivectors]] have grade 2, and [[trivectors]] have grade 3.

			== In the Book ==

			* Grade and antigrade are introduced in Section 2.1.4.

	== See Also ==		== See Also ==
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	* [[Duality]]		* [[Duality]]
	* [[Complements]]		* [[Complements]]

	~~== In the Book ==~~

	* Grade and antigrade are introduced in Section 2.1.4.

Eric Lengyel at 05:10, 13 April 2024

2024-04-13T05:10:43Z

← Older revision		Revision as of 05:10, 13 April 2024
Line 13:		Line 13:
	* [[Duality]]		* [[Duality]]
	* [[Complements]]		* [[Complements]]

			== In the Book ==

			* Grade and antigrade are introduced in Section 2.1.4.

Eric Lengyel: Created page with "The ''grade'' of a basis element in a geometric algebra is equal to the number of basis vectors present in its factorization. An arbitrary element whose components all have the same grade is also said to have that grade. The ''antigrade'' of a basis element is equal to the number of basis vectors absent from its factorization. The grade of an element $$\mathbf x$$ is denoted by $$\operatorname{gr}(\mathbf x)$$, and the antigrade is denoted by $$\operatorname{ag}(\mathb..."

2023-07-15T06:15:19Z

Created page with "The ''grade'' of a basis element in a geometric algebra is equal to the number of basis vectors present in its factorization. An arbitrary element whose components all have the same grade is also said to have that grade. The ''antigrade'' of a basis element is equal to the number of basis vectors absent from its factorization. The grade of an element $$\mathbf x$$ is denoted by $$\operatorname{gr}(\mathbf x)$$, and the antigrade is denoted by $$\operatorname{ag}(\mathb..."

New page

The ''grade'' of a basis element in a geometric algebra is equal to the number of basis vectors present in its factorization. An arbitrary element whose components all have the same grade is also said to have that grade.

The ''antigrade'' of a basis element is equal to the number of basis vectors absent from its factorization.

The grade of an element $$\mathbf x$$ is denoted by $$\operatorname{gr}(\mathbf x)$$, and the antigrade is denoted by $$\operatorname{ag}(\mathbf x)$$. In an ''n''-dimensional geometric algebra, it is always the case that

:$$\operatorname{gr}(\mathbf x) + \operatorname{ag}(\mathbf x) = n$$ .

[[Scalars]] have grade 0, and [[antiscalars]] have grade ''n''. [[Vectors]] have grade 1, and [[antivectors]] have antigrade 1. [[Bivectors]] have grade 2, and [[trivectors]] have grade 3.

== See Also ==

* [[Duality]]
* [[Complements]]