nLab linear isomorphism

Contents

Context

Linear algebra

homotopy theory, (∞,1)-category theory, homotopy type theory

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

models: topological, simplicial, localic, …

see also algebraic topology

Introductions

Definitions

Paths and cylinders

Homotopy groups

Basic facts

Theorems

Equality and Equivalence

Contents

Idea

A linear isomophism is a linear endomorphism VVV \to V (on some linear space VV) which is an isomorphism (in the given ambient category of modules/category of vector spaces), hence which has an inverse function that is also a linear map.

The group formed by linear isomorphisms under their composition is called the general linear group GL(V)GL(V) of the given linear space VV.

Last revised on September 21, 2024 at 14:07:41. See the history of this page for a list of all contributions to it.