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How to evaluate Nonorthogonal basis?

  1. Jul 29, 2008 #1
    hi all~
    How to evaluate the performance of a set of nonorthogonal basis?
    Like one in Hibert space which is most likely to be a nonorthongal set.
    Does it have any advantage compared with orthogonal ones in any aspects?

    i dont even know every to get started:confused:
     
  2. jcsd
  3. Jul 30, 2008 #2

    HallsofIvy

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    I am not sure what you mean by "evaluate". "Orthonormal" bases have the nice property that the coefficient of the basis vector [itex]\vec{e}_i[/itex] in the expansion of [itex]\vec{v}[/itex] is just the dot product: [itex]\vec{e}_i\cdot\vec{v}[/itex].

    Other than that, there is nothing special about orthogonal bases.
     
  4. Jul 30, 2008 #3

    thx:)

    i mean whether there is any kind of measurement which can be used to evaluate any aspect of a set of basis vectors.
    i.e. we can use reconstruction error to evaluate the descriptive ability of a set of basis vectors.(The only way i know)

    i havnt learned much on this aspect and i have searched on wikipedia for a long time with no progress.:frown:

    i dont know whether i have made my question clear.
    sry for my poor eng.:biggrin:
     
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