Recent content by cezarion

Thank you for your reply. I think I understand your example for L = xy. If instead I take M = xy + yz can I write M = \frac{1}{2}(x + y)^2 - \frac{1}{2}(x - y)^2 + \frac{1}{2}(y + z)^2 - \frac{1}{2}(y - z)^2? We haven't covered eigenvalues yet in our course, so I'm not sure how to apply that...

Thank you for your reply. The definition that I am supposed to use is given by http://mathworld.wolfram.com/QuadraticFormSignature.html I am not sure how to convert my linear series of terms into a signature though, seeing as how there are no squared terms.

I was just wondering if somebody could give me a very quick definition and work through a short example. We have just covered quadratic forms, and one of the questions we have been given is on calculating signatures. I found several online references that say the signature relates to the...

Thank you for the reply. This was actually proved in our textbook, so I am just citing the result in the proof for this problem, leaving just the general case that needs to be proved.

Homework Statement Prove that if all partial derivatives up to order n are zero at \vec{x} and f(x) = 0 then \displaystyle\lim_{h \rightarrow 0} \dfrac{f(x + h)}{|h|^n} = 0 Homework Equations \displaystyle\lim_{h \rightarrow 0} \dfrac{f(x + h) - f(x)}{|h|} = 0 f(x) = 0 The Attempt...