Quadratic Form

Treadstone 71

"Let Q(v)=<v,v> be the quadratic form associated to a real or hermitian inner product space. ... "

What's a quadratic form?

quasar987

try wiki and mathworld first

http://en.wikipedia.org/wiki/Quadratic_form

Treadstone 71

So it's LITERALLY <v,v>?

TD

In my lineair algebra course, it was defined like this (for the real case):

I suppose you know what a billineair map is.
If there is such a billineair map [itex]b:E \times E \to \mathbb{R}[/itex], where E is an n-dimensional Euclidean space, then we can define a map [itex]q:E \to \mathbb{R}[/itex] as [itex]q\left( {\vec x} \right) = b\left( {\vec x,\vec x} \right)[/itex].

We call this q the quadratic form, associated to the billineair map b.

So in general, we have then:

[tex]q\left( {\vec x} \right) = \sum\limits_{i = 1}^n {\sum\limits_{j = 1}^n {a_{ij} x_i x_j } } [/tex]