(Note: this isn't a homework question, I'm reviewing and I think the textbook is wrong.)(adsbygoogle = window.adsbygoogle || []).push({});

I'm working through the Gram-Schmidt process in my textbook, and at the end of every chapter it starts the problem set with a series of true or false questions. One statement is:

-Every orthogonal set is linearly independent. ->My answer:True; Text: False

What's the deal? I thought orthogonality => linear independence. I know if the statement was the other way around then it would be false, since Linear independence =/> orthogonality.

I'd usually write it off as a typo, but the next statement is:

-Every orthonormal set is linearly independent,

which is true in my opinion and the text's, and that makes me think that there's a distinction being pointed out between orthogonal sets and orthonormal sets that I've missed.

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# Linear independence of orthogonal and orthonormal sets?

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