Hermitian form over a division ring
Let be a division ring admitting an involution (http://planetmath.org/Involution2) . Let be a vector space over . A Hermitian form over is a function from to , denoted by with the following properties, for any and :
is additive in each of its arguments,
Note that if the Hermitian form is non-trivial and if is the identity on , then is a field and is just a symmetric bilinear form.
If we replace the last condition by , then over is called a skew Hermitian form.
Remark. Every skew Hermitian form over a division ring induces a Hermitian form and vice versa.
|Title||Hermitian form over a division ring|
|Date of creation||2013-03-22 15:41:04|
|Last modified on||2013-03-22 15:41:04|
|Last modified by||CWoo (3771)|
|Defines||skew Hermitian form|