linear isomorphism
Definition 1.
Suppose $V$ and $W$ are vector spaces^{} and $L\mathrm{:}V\mathrm{\to}W$ is a linear map. Then $L$ is a linear isomorphism if $L$ is bijective^{}.
Properties

1.
Compositions^{} and of linear isomorphisms is a linear isomorphism.

2.
The inverse^{} of a linear isomorphisms is a linear isomorphism.

3.
If either $V$ or $W$ if finite dimensional, then $dimV=dimW$. (This is a consequence of the ranknullity theorem^{}.)
Title  linear isomorphism 

Canonical name  LinearIsomorphism 
Date of creation  20130322 14:36:42 
Last modified on  20130322 14:36:42 
Owner  matte (1858) 
Last modified by  matte (1858) 
Numerical id  7 
Author  matte (1858) 
Entry type  Definition 
Classification  msc 15A04 
Synonym  invertible linear map 
Synonym  bijective linear map 
Synonym  nonsingular linear map 