- #1
larusi
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Hi, I'm reading up on linear algebra and I'm wondering if the remark after a theorem I'm reading here is complete. The theorem states:
"If {V_1,V_2,...,V_k} is an orthogonal set of nonzero vectors then these vectors are linearly independent."
Remark after that simply states that if a set of vectors are linearly independent they are not necessarily orthogonal.
If the dimension you're working with is R^n I find that if you have a set of 2*n linearly independent vectors in that dimension then they are necessarily orthogonal. Am I thinking about this the wrong way?
"If {V_1,V_2,...,V_k} is an orthogonal set of nonzero vectors then these vectors are linearly independent."
Remark after that simply states that if a set of vectors are linearly independent they are not necessarily orthogonal.
If the dimension you're working with is R^n I find that if you have a set of 2*n linearly independent vectors in that dimension then they are necessarily orthogonal. Am I thinking about this the wrong way?