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

Determine the definiteness of the following constrained quadratic:

Q(x_{1},x_{2}) = x_{1}^{2}+2x_{1}x_{2}- x_{2}^{2}subject to x_{1}+ x_{2}= 0

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- Aug 7th 2012, 08:34 AMbublemjjDefiniteness 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(x_{1},x_{2}) = x_{1}^{2}+2x_{1}x_{2}- x_{2}^{2}subject to x_{1}+ x_{2}= 0 - Aug 7th 2012, 08:39 AMrichard1234Re: Definiteness of Constrained Quadratics - HELP
Don't know what "definiteness" is (in a mathematical sense) but if you replace $\displaystyle x_2$ with $\displaystyle -x_1$ you obtain

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

$\displaystyle Q(x_1, x_2) = -2x_1^2$. - Aug 7th 2012, 09:40 AMtom@ballooncalculusRe: 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:

http://www.google.co.uk/url?sa=t&rct...pRi9Hw&cad=rja

Also,

http://www.google.co.uk/url?sa=t&rct...nnH_gElX-UjLNA

Positive definiteness - Wikipedia, the free encyclopedia - Aug 7th 2012, 09:55 AMbublemjjRe: Definiteness of Constrained Quadratics - HELP