Vector multiplication

Index of articles associated with the same name

In mathematics, vector multiplication may refer to one of several operations between two vectors. It may concern any of the following articles:Dot product – also known as the "scalar product", a binary operation that takes two vectors and returns a scalar quantity. The dot product of two vectors can be defined as the product of the magnitudes of the two vectors and the cosine of the angle between the two vectors. Alternatively, it is defined as the product of the projection of the first vector onto the second vector and the magnitude of the second vector. Thus, 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 between the two vectors. So, if is the unit vector perpendicular to the plane determined by vectors and , Exterior product or wedge product – a binary operation on two vectors that results in a bivector. In Euclidean 3-space, the wedge product has the same magnitude as the cross product but generalizes to arbitrary affine spaces and products between more than two vectors. Tensor product – for two vectors and where and are vector spaces, their tensor product belongs to the tensor product of the vector spaces. Geometric product or Clifford product – for two vectors, the geometric product is a mixed quantity consisting of a scalar plus a bivector. The geometric product is well defined for any multivectors as arguments. A bilinear product in an algebra over a field. A Lie bracket for vectors in a Lie algebra. Hadamard product – entrywise or elementwise product of tuples of scalar coordinates, where . Outer product - where with results in a matrix. Triple products – products involving three vectors. Quadruple products – products involving four vectors.

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