1. Feb 22, 2010

### player1_1_1

1. The problem statement, all variables and given/known data
$$x^2-xy+y^2$$
how can I check if this form has always same sign (+ or -)?

2. Feb 23, 2010

### Tinyboss

It's non-negative for all x,y, and 0 only at 0,0. Suppose |x|<|y|. Then |xy|<y^2, and the expression is positive. Likewise if |y|<|x|.

3. Feb 28, 2010

### player1_1_1

i heard about silvester method (with det), how i can solve this with this method?

4. Feb 28, 2010

### Dick

Represent the form as a matrix, M, so x^(T)Mx is your quadratic form. Then find the eigenvalues of M.

5. Feb 28, 2010

### player1_1_1

well, I know that:) but why this form is represented by this matrix? why this form is defined when its more than 0 and no defined when less? and what can I do when det is 0?

6. Feb 28, 2010

### Dick

I think the answers would be a lot clearer if you actually tried to do the problem. What is the matrix M and what are it's eigenvalues? It only has two and they are both positive.