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If nonzero vectors are mutually orthogonal, then those vectors are linearly independent.
Then if those nonzero vectors are linearly independent, they are orthogonal to each other?
These two statements have iff relation?

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  • $\begingroup$ Imagine two arrows with an angle of 45 degrees between them. $\endgroup$ – wj32 Dec 2 '12 at 9:03
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    $\begingroup$ I found counter example $x_1=(1, 0), x_2=(2, 1)$, they are linearly independent but not orthogonal. So the inverse is not true, right? $\endgroup$ – email Dec 2 '12 at 9:09
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    $\begingroup$ That’s right; the implication goes only in one direction. $\endgroup$ – Brian M. Scott Dec 2 '12 at 9:12
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This post is made community wiki in order to remove this question from the "unanswered" list.


As already mentioned in the comments, this is not an "if and only if" relation. For example $x_1=(1,0)$ and $x_2=(2,1)$ are linearly independent but not orthogonal.

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