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In exterior algebra and geometric algebra the exterior product of two vectors is a bivector, ... The vector triple product is defined as the cross product of one ...
For example, the inner product of a polar vector and an axial vector resulting from the cross product in the triple product should result in a pseudoscalar, a result which is more obvious if the calculation is framed as the exterior product of a vector and bivector. They generalise to other dimensions; in particular bivectors can be used to ...
The cross product and triple product in three dimensions each admit both geometric and algebraic interpretations. The cross product u × v can be interpreted as a vector which is perpendicular to both u and v and whose magnitude is equal to the area of the parallelogram determined by the two vectors.
Like the geometric product of two vectors, this geometric product can be grouped into symmetric and antisymmetric parts, one of which is a pure k-vector. In analogy the antisymmetric part of this product can be called a generalized dot product, and is roughly speaking the dot product of a "plane" (bivector), and a vector.
Since the geometric product and the exterior product are equal on orthogonal vectors, this grading can be conveniently constructed by using an orthogonal basis {, …,} . Elements of the geometric algebra that are scalar multiples of 1 {\displaystyle 1} are of grade 0 {\displaystyle 0} and are called scalars .
We go through a lot of nuts in my house. My husband adds walnuts, almonds and pecans to his oatmeal and chia pudding, plus we snack on pistachios, cashews and mixed nuts.I always get them at ...
The dot product takes in two vectors and returns a scalar, while the cross product [a] returns a pseudovector. Both of these have various significant geometric interpretations and are widely used in mathematics, physics, and engineering. The dyadic product takes in two vectors and returns a second order tensor called a dyadic in this context. A ...
Casu marzu is registered as a traditional product of Sardinia and therefore is locally protected. Still, it has been deemed illegal by the Italian government since 1962 due to laws that prohibit ...