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cookiesyum
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Homework Statement
Let the quadratic form F(x,y,z) be given as
F(x,y,z) = 2x^2 + 3y^2 + 5z^2 - xy -xz - yz.
Find the transitional matrix that would transform this form to a diagonal form.
Homework Equations
A quadratic form is a second degree polynomial equation in three variables which has the form
F(x,y,z) = ax^2 + by^2 + cz^2 + 2dxy + 2exz + 2fyz
where coefficients a through i are real numbers.
The curve F(x,y,z) = j can be written in the form (x^T)*A*x = j where
x = [x, y, z]
A = [a, d, e]
[d, b, f]
[e, f, c]
The Attempt at a Solution
I need to find the eigenvectors of (A-sI) to form the transitional matrix. Does (x^T)*A*x = j have anything to do with finding this matrix? Having trouble picturing all of this...