Thread: 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

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



.

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

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:

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

Thank you SOOO MUCH. The pdf does help a lot!!!
May I ask for one more favour?
Do you have a similar pdf related to "Continuous Differentiable Function" - kind of answering questions like whether a function is C^1 or C^k?
You will be my life-saver.