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Math Help - Orthogonality

  1. #1
    Junior Member
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    Orthogonality

    Would does it mean to say that two matrices or functions are orthogonal? What does this signify?
    I suppose it depends on the inner product. Say if the inner product is the trace of A(^T)B.
    Is there a real life application of orthogonal vectors in these sort of vector spaces?
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  2. #2
    A Plied Mathematician
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    Re: Orthogonality

    It looks like you've answered your own question. As for real life applications, function orthogonality is used all over the place in differential equations, where, say, the orthonormal basis (that's a set of functions) of an Hermitian operator is used to write down the solution to the DE. Matrix orthogonality, in a like manner, might be used in a discretization of the same problem, I suppose, though I don't know for sure.
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