canonical basis for symmetric bilinear forms
Recall that a bilinear form has a well-defined rank, and denote this by .
If we may choose a basis such that , and , for some integers and , where . Furthermore, these integers are invariants of the bilinear form. This is known as Sylvester’s Law of Inertia. is positive definite if and only if , . Such a form constitutes a real inner product space.
If we may go further and choose a basis such that and , where .
If we may choose a basis such that ,
|Title||canonical basis for symmetric bilinear forms|
|Date of creation||2013-03-22 14:56:25|
|Last modified on||2013-03-22 14:56:25|
|Last modified by||Mathprof (13753)|
|Defines||Sylvester’s Law of Inertia|