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    (Original post by drandy76)
    And the I denotes which unit vector it denotes right, so e_3 would be equivalent to k?


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    Yep
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    (Original post by drandy76)
    From what I recall they're components? I'll check tomorrow and get back to you but I recall reading about them to show why vector addition works


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    Yeah, that's what I said, the i, j, k components are all perpendicular (orthogonal) to one another and form an orthonormal basis.
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    (Original post by Zacken)
    Yeah, that's what I said, the i, j, k components are all perpendicular (orthogonal) to one another and form an orthonormal basis.
    Are orthonormal basis' restricted to just 3 vectors or is it any set of vectors which are orthogonal to one another?


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    (Original post by drandy76)
    Are orthonormal basis' restricted to just 3 vectors or is it any set of vectors which are orthogonal to one another?


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    The set \{e_1, e_2, \cdots, e_n\} forms an orthonormal basis, so definitely not just 3 vectors. That would ruin the whole point of studying vector spaces.
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    (Original post by Zacken)
    The set \{e_1, e_2, \cdots, e_n\} forms an orthonormal basis, so definitely not just 3 vectors. That would ruin the whole point of studying vector spaces.
    oh i see, so the restriction is based upon the which space you're working in? so for example R^5 space would be restricted to no more than 5 unit vectors forming an orthonormal basis?
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    (Original post by drandy76)
    oh i see, so the restriction is based upon the which space you're working in? so for example R^5 space would be restricted to no more than 5 unit vectors forming an orthonormal basis?
    I'm not sure. So I'll let someone else step in, Rayquaza and clear it up. But I think that 5 unit vectors (linearly independent) would span the space \mathbb{R}^5. I'm not sure if you can have an orthonormal basis \{e_1, \cdots e_k\} for a space \mathbb{R}^n with k \neq n but I really don't know so I'm not going to say anything about it.
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    (Original post by Zacken)
    I'm not sure. So I'll let someone else step in, Rayquaza and clear it up. But I think that 5 unit vectors (linearly independent) would span the space \mathbb{R}^5. I'm not sure if you can have an orthonormal basis \{e_1, \cdots e_k\} for a space \mathbb{R}^n with k \neq n but I really don't know so I'm not going to say anything about it.
    Tried to google it but all i got were paragraphs about orientations in Euclidean space
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    i'm surprised this thread is still going xD
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    (Original post by drandy76)
    oh i see, so the restriction is based upon the which space you're working in? so for example R^5 space would be restricted to no more than 5 unit vectors forming an orthonormal basis?
    Hmm linear algebra isn't my best area of maths! But yeah I think R^5 would need 5 vectors to form the basis. But they don't need to be ones like (1,0,0,0,0), (0,1,0,0,0),etc you can have other weird ones as long as they are linearly independent.
 
 
 
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