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?
Linearly independent and orthogonality
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linear-algebra
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1That’s right; the implication goes only in one direction. – 2012-12-02
1 Answers
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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.