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
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
Don't know what "definiteness" is (in a mathematical sense) but if you replace $\displaystyle x_2$ with $\displaystyle -x_1$ you obtain
$\displaystyle Q(x_1, x_2) = x_1^2 + 2x_1(-x_1) - (-x_1)^2$
$\displaystyle Q(x_1, x_2) = -2x_1^2$.
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