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Homework Help: A question about orthgonal/orthonormal basis

  1. Feb 11, 2008 #1
    i added the question in the link


    my problem with this question starts with this W(and the T shape up side down) simbol

    it represents a vector which is perpandicular to W

    so why are they ask me to find the orthogonal(perpandicular) basis
    to that perpandicular to W vector??(its already perpandicular to W)

    so my answer should be the vectors of W
    but in the answer they extract the vectors
    from the formula and look for a vector which is perpandicular
    to both vectors of W

    if there were only W then i whould exract the vectors of the formula
    and using gramm shmit
    i would find the orghonormal basis(which includes in itself orthogonality)

    but i was ask to find the orthogonal vectors of this W (upsidedown T)

    i dont know what is the formula of its vectors??
    Last edited: Feb 11, 2008
  2. jcsd
  3. Feb 11, 2008 #2


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    Can you find vector(s) such that any and all vector(s) orthogonal to W can be expressed as a linear combination of these basis vectors?
  4. Feb 11, 2008 #3


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    You seem to be interpreting "orthogonal basis" for [itex]W^{\perp}[/itex] as meaning vectors perpendicular to [itex]W^{\perp}[/itex]! That's not correct. An "orthogonal basis" for a vector space, V, consists of vectors in V that are perpendicular to on another. For example, if the overall vector space is R3 and W is the z-axis, then [itex]W^{\perp}[/itex] is the xy-plane. An "orthonormal" basis for that is {(1, 0, 0), (0, 1, 0)}.

    We can't answer that without knowing precisely what W is.
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