Reduce the following quadratic form to canonical form.

• Jan 30th 2013, 11:02 AM
brianbrian
Reduce the following quadratic form to canonical form.
I encountered next and the last problem from algebra, I hope you will be able to help me, because my books aren't enough to explain this for me :)

Reduce the following quadratic form to canonical form. Express the new variables in terms of
the old ones.
f(x, y, z) = x^2 + 4y^2 + 3z^2 + 4xy − 6xz + 4yz
• Jan 30th 2013, 11:59 AM
FernandoRevilla
Re: Reduce the following quadratic form to canonical form.
Quote:

Originally Posted by brianbrian
I encountered next and the last problem from algebra, I hope you will be able to help me, because my books aren't enough to explain this for me :)

Reduce the following quadratic form to canonical form. Express the new variables in terms of
the old ones.
f(x, y, z) = x^2 + 4y^2 + 3z^2 + 4xy − 6xz + 4yz

There are several ways to solve the problem, Gauss method, orthogonal diagonalization, elementary transformatios (rows and columns),... .What method have you covered?
• Jan 30th 2013, 12:02 PM
brianbrian
Re: Reduce the following quadratic form to canonical form.
So this should be solved as matrix? I am familliar with gauss method.