Publication

The Chu Construction For Complete Atomistic Coatomistic Lattices

Gavin Jay Seal, Boris Ischi
2013
Journal Articles

Abstract

The Chu construction is used to define a *-autonomous structure on a category of complete atomistic coatomistic lattices. This construction leads to a new tensor product that is compared with a certain number of other existing tensor products.

Official source

https://infoscience.epfl.ch/entities/publication/74305075-aa6f-4d71-82e3-71e5832185fe

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Gavin Jay Seal, Boris Ischi
2013
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/74305075-aa6f-4d71-82e3-71e5832185fe

About this result

Related concepts (8)

Tensor product

In mathematics, the tensor product of two vector spaces V and W (over the same field) is a vector space to which is associated a bilinear map that maps a pair to an element of denoted An element of the form is called the tensor product of v and w. An element of is a tensor, and the tensor product of two vectors is sometimes called an elementary tensor or a decomposable tensor. The elementary tensors span in the sense that every element of is a sum of elementary tensors.

Tensor

In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors. There are many types of tensors, including scalars and vectors (which are the simplest tensors), dual vectors, multilinear maps between vector spaces, and even some operations such as the dot product.

Tensor contraction

In multilinear algebra, a tensor contraction is an operation on a tensor 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 of the tensor(s) caused by applying the summation convention to a pair of dummy indices that are bound to each other in an expression. The contraction of a single mixed tensor occurs when a pair of literal indices (one a subscript, the other a superscript) of the tensor are set equal to each other and summed over.

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