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and a 2-vector. A sum of only k-grade components is called a k-vector, or a homogeneous multivector.

The highest grade element in a space is called a pseudoscalar.

If a given element is homogeneous of a grade k, then it is a k-vector, but not necessarily a k-blade. Such an element is a k-blade when it can be expressed as the exterior product of k vectors. A geometric algebra generated by a four-dimensional vector space illustrates the point with an example: The sum of any two blades with

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