Search results
Results From The WOW.Com Content Network
The scalar triple product (also called the mixed product, box product, or triple scalar product) is defined as the dot product of one of the vectors with the cross product of the other two. Geometric interpretation
The product B e 123 yields the bivector that is Hodge dual to B in three dimensions, as discussed above, while E e 4 as a product of orthogonal vectors is also bivector-valued. As a whole it is the electromagnetic tensor expressed more compactly as a bivector, and is used as follows.
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...
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.
In mathematics, the dot product or scalar product [note 1] is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. In Euclidean geometry , the dot product of the Cartesian coordinates of two vectors is widely used.
In mathematics, a geometric algebra (also known as a Clifford algebra) is an algebra that can represent and manipulate geometrical objects such as vectors. Geometric algebra is built out of two fundamental operations, addition and the geometric product. Multiplication of vectors results in higher-dimensional objects called multivectors ...
the dyadic product of two vectors and is denoted by (juxtaposed; no symbols, multiplication signs, crosses, dots, etc.) the outer product of two column vectors a {\displaystyle \mathbf {a} } and b {\displaystyle \mathbf {b} } is denoted and defined as a ⊗ b {\displaystyle \mathbf {a} \otimes \mathbf {b} } or a b T {\displaystyle \mathbf {a ...
The two common operators, a dot and a rotated cross, are also acceptable (although the rotated cross is almost never used), but they risk confusion with dot products and cross products, which operate on two vectors. The product of a scalar k with a vector v can be represented in any of the following fashions: