Derived tensor product information

a differential graded algebra A over a commutative ring R, the derived tensor product functor is − ⊗ A L − : D ( M A ) × D ( A M ) → D ( R M ) {\displaystyle...

v\otimes w} is called the tensor product of v and w. An element of V ⊗ W {\displaystyle V\otimes W} is a tensor, and the tensor product of two vectors is sometimes...

of differential operators. Tor functor Tensor product of algebras Tensor product of fields Derived tensor product Tensoring with M the exact sequence 0...

individual left derived functors one can also take the total derived functor of the tensor functor. This gives rise to the derived tensor product − ⊗ L − :...

In mathematics, tensor calculus, tensor analysis, or Ricci calculus is an extension of vector calculus to tensor fields (tensors that may vary over a manifold...

mathematics, specifically multilinear algebra, a dyadic or dyadic tensor is a second order tensor, written in a notation that fits in with vector algebra[disambiguation...

{\displaystyle n} and a tensor of order m {\displaystyle m} is a tensor of order n + m − 2 {\displaystyle n+m-2} , see Tensor contraction for details...

Tensor networks or tensor network states are a class of variational wave functions used in the study of many-body quantum systems. Tensor networks extend...

electromagnetism, the electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a...

of tensor theory. For expositions of tensor theory from different points of view, see: Tensor Tensor (intrinsic definition) Application of tensor theory...

cross product can be seen as the (1,2)-tensor (a mixed tensor, specifically a bilinear map) obtained from the 3-dimensional volume form, a (0,3)-tensor, by...

structure tensor is often used in image processing and computer vision. For a function I {\displaystyle I} of two variables p = (x, y), the structure tensor is...

In mathematics, the Tor functors are the derived functors of the tensor product of modules over a ring. Along with the Ext functor, Tor is one of the central...

inertia tensor of a body calculated at its center of mass, and R {\displaystyle \mathbf {R} } be the displacement vector of the body. The inertia tensor of...

}_{i_{r+p}}.} The components of this tensor are precisely the skew part of the components of the tensor product s ⊗ t, denoted by square brackets on the...

deformation tensors. In 1839, George Green introduced a deformation tensor known as the right Cauchy–Green deformation tensor or Green's deformation tensor (the...

differential geometry, the torsion tensor is a tensor that is associated to any affine connection. The torsion tensor is bilinear map of two input vectors...

tensor (symbol σ {\displaystyle {\boldsymbol {\sigma }}} , named after Augustin-Louis Cauchy), also called true stress tensor or simply stress tensor...

consequently a vector is called a contravariant tensor. A vector, which is an example of a contravariant tensor, has components that transform inversely to...

differentiable manifold. Functions, tensor fields and forms can be differentiated with respect to a vector field. If T is a tensor field and X is a vector field...

\otimes K_{s_{r}}} where ⊗ {\displaystyle \otimes } denotes the derived tensor product of chain complexes of A-modules. When s 1 , … , s r {\displaystyle...

a Cartesian tensor uses an orthonormal basis to represent a tensor in a Euclidean space in the form of components. Converting a tensor's components from...

, fiber product of immersions) does not yield the correct intersection number. In the derived context, one takes the derived tensor product A ⊗ L B {\displaystyle...