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Math Help - Orthonormalizing a set of functions (what??)

  1. #1
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    Orthonormalizing a set of functions (what??)

    Hi,

    One particular question in my assignment goes like this:
    "Use the Gram-Schmidt procedure in order to orthonormalize {2x, x^2, sin(x)}"

    What confuses me is the fact that the question asks me to perform the Gram-Schmidt procedure on something that's not a set of vectors.

    Is it even possible to project or normalize functions?

    Can somebody explain this?

    Thanks,
    - dadads -
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by dadads View Post
    Hi,

    One particular question in my assignment goes like this:
    "Use the Gram-Schmidt procedure in order to orthonormalize {2x, x^2, sin(x)}"

    What confuses me is the fact that the question asks me to perform the Gram-Schmidt procedure on something that's not a set of vectors.

    Is it even possible to project or normalize functions?

    Can somebody explain this?

    Thanks,
    - dadads -
    You need an inner product space for the Gram-Schmidt process, so we might consider the space of continuous functions on [0,1] with innerproduct defined by:

    \langle f,g \rangle=\int_0^1 f(x)g(x) \; dx

    Now you can apply the G-S process.

    (I am pretty sure that your assignment indicates the inner product you are supposed to use)

    RonL
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