Originally Posted by

**Hartlw** the vector **x** is the same in either basis. its representation by coordinates is different in different bases.

for example: **u** = x1**e**1 + x2**e**2 =x1'**e**1' + x2'**e**2'

Don't bother with primed coordinates. just make a note you are switching to eigenvector basis and the components are wrt that basis. The tip-off for switching to an eigenvector basis was that A is given as real and symmetric.

First solve the problem in the simple intelligible form:

f= [(ax^2+by^2]e^(x^2+y^2), x,y components of **x** in eigenvector system and a,b eigenvalues.

to see what happens. Then you can clean it up. I assume you can takle partials wrt x and y and set them equal to 0?