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  2. Dot product - Wikipedia

    en.wikipedia.org/wiki/Dot_product

    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.

  3. Vector algebra relations - Wikipedia

    en.wikipedia.org/wiki/Vector_algebra_relations

    The following are important identities in vector algebra.Identities that only involve the magnitude of a vector ‖ ‖ and the dot product (scalar product) of two vectors A·B, apply to vectors in any dimension, while identities that use the cross product (vector product) A×B only apply in three dimensions, since the cross product is only defined there.

  4. Vector calculus identities - Wikipedia

    en.wikipedia.org/wiki/Vector_calculus_identities

    In Cartesian coordinates, the divergence of a continuously differentiable vector field = + + is the scalar-valued function: ⁡ = = (, , ) (, , ) = + +.. As the name implies, the divergence is a (local) measure of the degree to which vectors in the field diverge.

  5. Triple product - Wikipedia

    en.wikipedia.org/wiki/Triple_product

    In geometry and algebra, the triple product is a product of three 3-dimensional vectors, usually Euclidean vectors.The name "triple product" is used for two different products, the scalar-valued scalar triple product and, less often, the vector-valued vector triple product.

  6. Vector notation - Wikipedia

    en.wikipedia.org/wiki/Vector_notation

    A scalar beside a vector (either or both of which may be in parentheses) implies scalar multiplication. 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 ...

  7. Vector multiplication - Wikipedia

    en.wikipedia.org/wiki/Vector_multiplication

    Cross product – also known as the "vector product", a binary operation on two vectors that results in another vector. The cross product of two vectors in 3-space is defined as the vector perpendicular to the plane determined by the two vectors whose magnitude is the product of the magnitudes of the two vectors and the sine of the angle ...

  8. Dyadics - Wikipedia

    en.wikipedia.org/wiki/Dyadics

    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 ...

  9. Scalar (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Scalar_(mathematics)

    A scalar is an element of a field which is used to define a vector space.In linear algebra, real numbers or generally elements of a field are called scalars and relate to vectors in an associated vector space through the operation of scalar multiplication (defined in the vector space), in which a vector can be multiplied by a scalar in the defined way to produce another vector.