Topic

Blade

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Overview

In the study of geometric algebras, a -blade or a simple -vector is a generalization of the concept of scalars and vectors to include simple bivectors, trivectors, etc. Specifically, a -blade is a -vector that can be expressed as the exterior product (informally wedge product) of 1-vectors, and is of grade . In detail: A 0-blade is a scalar. A 1-blade is a vector. Every vector is simple. A 2-blade is a simple bivector. Sums of 2-blades are also bivectors, but not always simple. A 2-blade may be expressed as the wedge product of two vectors and : A 3-blade is a simple trivector, that is, it may be expressed as the wedge product of three vectors , , and :

From Wikipedia (CC BY-SA 4.0).

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Overview

In the study of geometric algebras, a -blade or a simple -vector is a generalization of the concept of scalars and vectors to include simple bivectors, trivectors, etc. Specifically, a -blade is a -vector that can be expressed as the exterior product (informally wedge product) of 1-vectors, and is of grade . In detail: A 0-blade is a scalar. A 1-blade is a vector. Every vector is simple. A 2-blade is a simple bivector. Sums of 2-blades are also bivectors, but not always simple. A 2-blade may be expressed as the wedge product of two vectors and : A 3-blade is a simple trivector, that is, it may be expressed as the wedge product of three vectors , , and :

From Wikipedia (CC BY-SA 4.0).

Not who you're looking for? Others named Blade: sharp part of a weapon or cutting tool · Block All Drive-by Download Exploits, software developed at · 1973 film by Ernest Pintoff · New Line cinema franchise based on the fictional Marvel Comi