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Orthogonal set - Geometric interpretation

  1. Dec 19, 2012 #1
    Orthogonal set -- Geometric interpretation

    Hello,

    If we have two vectors u,v then in an inner product space, they are said to be orthogonal if <u,v>=0.

    Well, orthogonal means perpendicular in Euclidean space, i.e. 90 degrees. How <u,v> becomes zero.

    Secondly, if I have three vectors, v1,v2,v3 with certain values, computing, we get <v1,v2>=0
    <v1,v3>=0
    <v2,v3>=0

    How will it look like in geometrical figure. I mean to say, what if we take these 3 vectors and put it on a picture and how it would look like?

    Thanks,

    -- Shounak
     
  2. jcsd
  3. Dec 19, 2012 #2

    Erland

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    Re: Orthogonal set -- Geometric interpretation

    In R3, these will be three perpendicular vectors. For example, the standard basis vectors (1,0,0), (0,1,0), and (0,0,1).
    In R2, this is not possible, unless at least one of the vectors is the zero vector.
     
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