Bivektorer

Bivektorer are a fundamental concept in geometric algebra, a mathematical framework that generalizes vector spaces and linear algebra. They are elements of a geometric algebra that are formed by the outer product of two vectors. The outer product, also known as the wedge product, is a non-commutative operation that produces a bivector when applied to two vectors.

A bivector represents a directed area in a plane, defined by the two vectors used to create it. This makes bivectors particularly useful in describing planar orientations and rotations in three-dimensional space. In contrast to vectors, which have magnitude and direction, bivectors have magnitude and orientation but are not tied to a specific point in space.

Bivector algebra extends the properties of vector algebra, allowing for operations such as addition, scalar multiplication, and the outer product with other vectors or bivectors. This extension provides a powerful tool for handling geometric transformations and relationships in a unified manner.

Bivectors are closely related to the concept of the cross product in vector algebra, but they offer a more general and flexible framework. While the cross product is specific to three-dimensional space, bivectors can be defined in any dimension, making geometric algebra a versatile tool for both theoretical and applied mathematics.