nLab
Vect

Context

Monoidal categories

Linear algebra

Contents

Definition

Given a field kk, the category Vect kVect_k is category whose objects are vector spaces and whose morphisms are linear map.

If the field kk is understood, one often just writes VectVect.

The study of VectVect is called linear algebra.

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

This is a compact closed category (see here).

FinVect\Fin Vect is where most of ordinary linear algebra lives, although much of it makes sense in all of VectVect. See also at finite quantum mechanics in terms of dagger-compact categories.

On the other hand, anything involving transposes or inner products really takes place in FinFin Hilb.

category: category

Revised on July 21, 2014 00:16:21 by Urs Schreiber (82.113.106.220)