tensor rank
1Rank — is a very broad term with several meanings. As a noun it is usually related to a relative position or to some kind of ordering (see also ranking). As an adjective it is used to mean profuse, conspicuous, absolute, or unpleasant, especially in… …
2Rank (mathematics) — Rank means a wide variety of things in mathematics, including: * Rank (linear algebra) * Rank of a tensor * Rank of an abelian group * Rank of a Lie group * Percentile rank * Rank (differential topology) * Rank of a vector bundle * Rank (set… …
3Tensor (intrinsic definition) — For an introduction to the nature and significance of tensors in a broad context, see Tensor. 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… …
4Tensor product — In mathematics, the tensor product, denoted by otimes, may be applied in different contexts to vectors, matrices, tensors, vector spaces, algebras, topological vector spaces, and modules. In each case the significance of the symbol is the same:… …
5Rank (linear algebra) — The column rank of a matrix A is the maximum number of linearly independent column vectors of A. The row rank of a matrix A is the maximum number of linearly independent row vectors of A. Equivalently, the column rank of A is the dimension of the …
6Tensor — For other uses, see Tensor (disambiguation). Note that in common usage, the term tensor is also used to refer to a tensor field. Stress, a second order tensor. The tensor s components, in a three dimensional Cartesian coordinate system, form the… …
7Tensor contraction — In multilinear algebra, a tensor contraction is an operation on one or more tensors that arises from the natural pairing of a finite dimensional vector space and its dual. In components, it is expressed as a sum of products of scalar components… …
8Tensor algebra — In mathematics, the tensor algebra of a vector space V , denoted T ( V ) or T bull;( 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… …
9Tensor density — A tensor density transforms as a tensor, except that it is additionally multiplied or weighted by a power of the Jacobian determinant.For example, a rank 3 tensor density of weight W transforms as::A {ijk}^prime =egin{vmatrix} alpha… …
10Rank of an abelian group — In mathematics, the rank, or torsion free rank, of an abelian group measures how large a group is in terms of how large a vector space over the rational numbers one would need to contain it; or alternatively how large a free abelian group it can… …
