Is is true that $ z \in \mathbb{R}^n, \forall u,v \in \mathbb{R}^n, \langle u,z\rangle = \langle v,z\rangle \implies u = v $ i.e. if two inner products with fixed vector $ z $ are equal so that $ u $ and $ v $ are equals.
Inner products equality for one of vectors fixed
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linear-algebra
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0And a more subtle question: why $$ instead of $\langle u,z \rangle$? ;-) – 2012-10-22
2 Answers
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For cross products, the answer is "no".
However, based on your notation, and the fact that you're talking about $\mathbb{R}^n$ rather than $\mathbb{R}^3$ (cross product defined specifically for $n=3$), it seems you may actually be asking about the inner product.
In that case, the answer is still "no".
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0@RahulNarain the inner product. I did the edit. – 2012-10-24