Category of finite dimensional Hilbert spaces

Category of finite dimensional Hilbert spaces

In mathematics, the category FdHilb has all finite dimensional Hilbert spaces for objects and linear transformations between them.

Properties

This category
* is monoidal,
* possesses finite biproducts, and
* is dagger compact.


Wikimedia Foundation. 2010.

Игры ⚽ Нужно решить контрольную?

Look at other dictionaries:

  • Dagger compact category — In mathematics, dagger compact categories (or dagger compact closed categories) first appeared in 1989 in the work of Doplicher and Roberts on the reconstruction of compact topological group from their category of finite dimensional continuous… …   Wikipedia

  • Dagger symmetric monoidal category — A dagger symmetric monoidal category is a monoidal category which also possesses a dagger structure; in other words, it means that this category comes equipped not only with a tensor in the category theoretic sense but also with dagger structure… …   Wikipedia

  • List of category theory topics — This is a list of category theory topics, by Wikipedia page. Specific categories *Category of sets **Concrete category *Category of vector spaces **Category of graded vector spaces *Category of finite dimensional Hilbert spaces *Category of sets… …   Wikipedia

  • Outline of category theory — The following outline is provided as an overview of and guide to category theory: Category theory – area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as… …   Wikipedia

  • Dagger category — In mathematics, a dagger category (also called involutive category or category with involution [1][2]) is a category equipped with a certain structure called dagger or involution. The name dagger category was coined by Selinger[3]. Contents …   Wikipedia

  • David Hilbert — Hilbert redirects here. For other uses, see Hilbert (disambiguation). David Hilbert David Hilbert (1912) Born …   Wikipedia

  • List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… …   Wikipedia

  • Tannaka–Krein duality — In mathematics, Tannaka–Krein duality theory concerns the interaction of a compact topological group and its category of linear representations. Its natural extension to the non Abelian case is the Grothendieck duality theory. It extends an… …   Wikipedia

  • Tannaka-Krein duality — In mathematics, Tannaka Krein duality theory concerns the interaction of a compact topological group and its category of linear representations. It extends an important mathematical duality between compact and discrete commutative topological… …   Wikipedia

  • Vector space — This article is about linear (vector) spaces. For the structure in incidence geometry, see Linear space (geometry). Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”