- #1
Shoelace Thm.
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Homework Statement
Find constraints on [itex] a,b,c \in \mathbb{R} [/itex] such that [itex] \forall w_1,w_2,w_3 \in \mathbb{C} [/itex],
(1) [itex] x = |w_1|^2(1-c) + a|w_2|^2 + c|w_1+w_3|^2 + |w_3|^2(b-c) \ge 0 [/itex] and
(2) [itex] x=0 \Rightarrow w_1=w_2=w_3=0 [/itex].
Homework Equations
The Attempt at a Solution
I believe the solution is [itex] a>0, c = \mathbb{R_{+}} \setminus \{1\}, b>c [/itex], but I am not sure if there are stronger bounds. How can I know for sure?
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