Linear algebra again

1. Mar 23, 2006

stunner5000pt

Consider the equation x^2 + xy + y^2 = 1. Find a rotation so that the equation has no cross term.

here a=b=c=1 right
but how do i find an angle by which to rotate???
the text says the angle is pi/4... i dont know how they got that .. though

2. Mar 23, 2006

Galileo

Start by writing it as a matrix equation:

$$x^2+xy+y^2=\vec x^T A \vec x$$

3. Mar 23, 2006

HallsofIvy

Staff Emeritus
Once you have the A Galileo is talking about, find its eigenvalues and eigenvectors. The eigenvectors give the directions for the new axes.