linear isomorphism

Definition 1.

Suppose V and W are vector spacesMathworldPlanetmath and L:VW is a linear map. Then L is a linear isomorphism if L is bijectiveMathworldPlanetmathPlanetmath.


  1. 1.

    CompositionsMathworldPlanetmathPlanetmath and of linear isomorphisms is a linear isomorphism.

  2. 2.

    The inversePlanetmathPlanetmathPlanetmathPlanetmath of a linear isomorphisms is a linear isomorphism.

  3. 3.

    If either V or W if finite dimensional, then dimV=dimW. (This is a consequence of the rank-nullity theoremMathworldPlanetmath.)

Title linear isomorphism
Canonical name LinearIsomorphism
Date of creation 2013-03-22 14:36:42
Last modified on 2013-03-22 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 non-singular linear map