1. ## Definiteness of Constrained Quadratics - HELP

I am so stuck with these questions. Great appreciation for any help! Thanks

Determine the definiteness of the following constrained quadratic:
Q(x1,x2) = x12 +2x1x2 - x22 subject to x1 + x2 = 0

2. ## Re: Definiteness of Constrained Quadratics - HELP

Don't know what "definiteness" is (in a mathematical sense) but if you replace $x_2$ with $-x_1$ you obtain

$Q(x_1, x_2) = x_1^2 + 2x_1(-x_1) - (-x_1)^2$

$Q(x_1, x_2) = -2x_1^2$.

3. ## Re: Definiteness of Constrained Quadratics - HELP

If it's any use, you get a 'no, not positive definite' from testing by plugging the coefficients into the matrix shown in the result at the top of this pdf:

Also,

Positive definiteness - Wikipedia, the free encyclopedia

4. ## Re: Definiteness of Constrained Quadratics - HELP

Originally Posted by tom@ballooncalculus
You get a 'no, not positive definite' from testing by plugging the coefficients into the matrix shown in the result at the top of this pdf: