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Vector multiplication, the Glossary

Index Vector multiplication

In mathematics, vector multiplication may refer to one of several operations between two (or more) vectors.[1]

Table of Contents

  1. 27 relations: Affine space, Algebra over a field, Angular momentum, Bivector, Clifford algebra, Cross product, Dot product, Euclidean vector, Exterior algebra, Geometric algebra, Hadamard product (matrices), Lie algebra, Lorentz force, Mathematics, Matrix multiplication, Multivector, Outer product, Rotation, Scalar (mathematics), Scalar multiplication, Tensor product, Torque, Triple product, Tuple, Vector algebra relations, Vector space, Work (physics).

  2. Multiplication
  3. Operations on vectors
  4. Set index articles on mathematics

Affine space

In mathematics, an affine space is a geometric structure that generalizes some of the properties of Euclidean spaces in such a way that these are independent of the concepts of distance and measure of angles, keeping only the properties related to parallelism and ratio of lengths for parallel line segments.

See Vector multiplication and Affine space

Algebra over a field

In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product.

See Vector multiplication and Algebra over a field

Angular momentum

Angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of linear momentum.

See Vector multiplication and Angular momentum

Bivector

In mathematics, a bivector or 2-vector is a quantity in exterior algebra or geometric algebra that extends the idea of scalars and vectors.

See Vector multiplication and Bivector

Clifford algebra

In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure of a distinguished subspace.

See Vector multiplication and Clifford algebra

Cross product

In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here E), and is denoted by the symbol \times. Vector multiplication and cross product are operations on vectors.

See Vector multiplication and Cross product

Dot product

In mathematics, the dot product or scalar productThe term scalar product means literally "product with a scalar as a result". Vector multiplication and dot product are operations on vectors.

See Vector multiplication and Dot product

Euclidean vector

In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction.

See Vector multiplication and Euclidean vector

Exterior algebra

In mathematics, the exterior algebra or Grassmann algebra of a vector space V is an associative algebra that contains V, which has a product, called exterior product or wedge product and denoted with \wedge, such that v\wedge v.

See Vector multiplication and Exterior algebra

Geometric algebra

In mathematics, a geometric algebra (also known as a Clifford algebra) is an extension of elementary algebra to work with geometrical objects such as vectors.

See Vector multiplication and Geometric algebra

Hadamard product (matrices)

In mathematics, the Hadamard product (also known as the element-wise product, entrywise product or Schur product) is a binary operation that takes in two matrices of the same dimensions and returns a matrix of the multiplied corresponding elements.

See Vector multiplication and Hadamard product (matrices)

Lie algebra

In mathematics, a Lie algebra (pronounced) is a vector space \mathfrak g together with an operation called the Lie bracket, an alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g, that satisfies the Jacobi identity.

See Vector multiplication and Lie algebra

Lorentz force

In physics, specifically in electromagnetism, the Lorentz force law is the combination of electric and magnetic force on a point charge due to electromagnetic fields.

See Vector multiplication and Lorentz force

Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

See Vector multiplication and Mathematics

Matrix multiplication

In mathematics, particularly in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. Vector multiplication and matrix multiplication are multiplication.

See Vector multiplication and Matrix multiplication

Multivector

In multilinear algebra, a multivector, sometimes called Clifford number or multor, is an element of the exterior algebra of a vector space.

See Vector multiplication and Multivector

Outer product

In linear algebra, the outer product of two coordinate vectors is the matrix whose entries are all products of an element in the first vector with an element in the second vector. Vector multiplication and outer product are operations on vectors.

See Vector multiplication and Outer product

Rotation

Rotation or rotational motion is the circular movement of an object around a central line, known as axis of rotation.

See Vector multiplication and Rotation

Scalar (mathematics)

A scalar is an element of a field which is used to define a vector space.

See Vector multiplication and Scalar (mathematics)

Scalar multiplication

In mathematics, scalar multiplication is one of the basic operations defining a vector space in linear algebra (or more generally, a module in abstract algebra). Vector multiplication and scalar multiplication are multiplication and operations on vectors.

See Vector multiplication and Scalar multiplication

Tensor product

In mathematics, the tensor product V \otimes W of two vector spaces and (over the same field) is a vector space to which is associated a bilinear map V\times W \rightarrow V\otimes W that maps a pair (v,w),\ v\in V, w\in W to an element of V \otimes W denoted. Vector multiplication and tensor product are operations on vectors.

See Vector multiplication and Tensor product

Torque

In physics and mechanics, torque is the rotational analogue of linear force.

See Vector multiplication and Torque

Triple product

In geometry and algebra, the triple product is a product of three 3-dimensional vectors, usually Euclidean vectors. Vector multiplication and triple product are operations on vectors.

See Vector multiplication and Triple product

Tuple

In mathematics, a tuple is a finite sequence or ordered list of numbers or, more generally, mathematical objects, which are called the elements of the tuple.

See Vector multiplication and Tuple

Vector algebra relations

The following are important identities in vector algebra. Vector multiplication and vector algebra relations are operations on vectors.

See Vector multiplication and Vector algebra relations

Vector space

In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called ''vectors'', can be added together and multiplied ("scaled") by numbers called ''scalars''.

See Vector multiplication and Vector space

Work (physics)

In science, work is the energy transferred to or from an object via the application of force along a displacement.

See Vector multiplication and Work (physics)

See also

Multiplication

Operations on vectors

Set index articles on mathematics

References

[1] https://en.wikipedia.org/wiki/Vector_multiplication

Also known as Multiplication of vectors.