Vect

Given a field $k$, the category **$Vect_k$** is category whose objects are vector spaces and whose morphisms are linear map.

If the field $k$ is understood, one often just writes $Vect$.

The study of $Vect$ is called linear algebra.

The full subcategory of Vect consisting of finite-dimensional vector spaces is denoted **$\Fin Vect$**.

$\Fin Vect$ is where most of ordinary linear algebra lives, although much of it makes sense in all of $Vect$. On the other hand, anything involving transposes or inner products really takes place in $Fin$ Hilb.

category: category

Revised on September 7, 2010 05:57:57
by Urs Schreiber
(134.100.32.213)