Answer: Is <-x,-x> Equal to <x,x>?

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The equality of the vectors <-x, -x> and is context-dependent. When considering them as 2-dimensional vectors, the equality holds true only when x equals 0; otherwise, <-x, -x> equals -. In the context of inner products within a vector space, the equality is valid, as <-x, -x> simplifies to . Thus, the interpretation of the notation determines the outcome.

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Is <-x,-x> = <x,x> !?

Thanks!
 
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That depends on what you mean by <x, x>!

Some people use it to mean a 2 vector. In that case, <-x, -x>= <x, x> only if x= 0. Other wise, <-x, -x>= -<x, x>.

But you may be referring to an inner product in some vector space. If that is so, then <-x, -x>= -< x, -x> = -(-<x, x>)= <x, x> so that is, in fact, true.
 

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