Hermitian form

A sesquilinear formPlanetmathPlanetmath over a pair of complex vector spaces (V,W) is a function B:V×W satisfying the following properties:

  1. 1.


  2. 2.


  3. 3.


for all 𝐯,𝐯1,𝐯2V, 𝐰,𝐰1,𝐰2W, and c,d. The vector spacesMathworldPlanetmath V and W are often identical, although the definition does not require them to be the same vector space.

A sesquilinear form B:V×V over a single vector space V is called a Hermitian form if it is complex conjugateMathworldPlanetmath symmetricPlanetmathPlanetmath: namely, if B(𝐯1,𝐯2)=B(𝐯2,𝐯1)¯.

An inner productMathworldPlanetmath over a complex vector space is a positive definitePlanetmathPlanetmath Hermitian form.

Title Hermitian form
Canonical name HermitianForm
Date of creation 2013-03-22 12:25:47
Last modified on 2013-03-22 12:25:47
Owner djao (24)
Last modified by djao (24)
Numerical id 8
Author djao (24)
Entry type Definition
Classification msc 47A07
Classification msc 15A63
Classification msc 11E39
Synonym sesquilinear form
Synonym sesqui-linear form
Related topic InnerProduct