# Quadratic surfaces + principle axes

1. Sep 28, 2011

### JamesGoh

In my lecture notes, one of the example problems involving a quadratic surface uses the
following method to generate the principle axes

Q.(1,0,0)^T for the x-axis

Q.(0,1,0^T for the y-axis

Q.(0,0,1)^T for the z-axis

note Q is a 3x3 orthogonal matrix (which im assuming contains the eigenvectors of the original 3x3 matrix)

To give this some reasoning, do we do Q.(1,0,0)^T to find principle x-axis since x is what we are only interested in (which explains the multiplication of Q by (1,0,0)^T )?

Likewise does this same logic work in the case of the principal y and z-axis ?

thanks