Search results
Results from the WOW.Com Content Network
The definition of a tensor as a multidimensional array satisfying a transformation law traces back to the work of Ricci. [1] An equivalent definition of a tensor uses the representations of the general linear group. There is an action of the general linear group on the set of all ordered bases of an n-dimensional vector space.
In machine learning, the term tensor informally refers to two different concepts (i) a way of organizing data and (ii) a multilinear (tensor) transformation. Data may be organized in a multidimensional array (M-way array), informally referred to as a "data tensor"; however, in the strict mathematical sense, a tensor is a multilinear mapping over a set of domain vector spaces to a range vector ...
In mathematics, the tensor algebra of a vector space V, denoted T(V) or T • (V), is the algebra of tensors on V (of any rank) with multiplication being the tensor product.It is the free algebra on V, in the sense of being left adjoint to the forgetful functor from algebras to vector spaces: it is the "most general" algebra containing V, in the sense of the corresponding universal property ...
In mathematics, the modern component-free approach to the theory of a tensor views a tensor as an abstract object, expressing some definite type of multilinear concept. Their properties can be derived from their definitions, as linear maps or more generally; and the rules for manipulations of tensors arise as an extension of linear algebra to multilinear algebra.
The outer product of tensors is also referred to as their tensor product, and can be used to define the tensor algebra. The outer product contrasts with: The dot product (a special case of " inner product "), which takes a pair of coordinate vectors as input and produces a scalar
In mathematics, specifically multilinear algebra, a dyadic or dyadic tensor is a second order tensor, written in a notation that fits in with vector algebra. There are numerous ways to multiply two Euclidean vectors .
In mathematics, a tensor is a certain kind of geometrical entity and array concept. It generalizes the concepts of scalar , vector and linear operator , in a way that is independent of any chosen frame of reference .
Tensor calculus has many applications in physics, engineering and computer science including elasticity, continuum mechanics, electromagnetism (see mathematical descriptions of the electromagnetic field), general relativity (see mathematics of general relativity), quantum field theory, and machine learning.