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Math Help - Orthogonal to Space Spanned By...

  1. #1
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    Orthogonal to Space Spanned By...

    Could some one tell me how to get started on this problem?

    Find the space orthogonal to the space spanned by \left \{ x^{3}, x+1 \right \} with respect to the inner product as defined by: <f, g> = \int_{1}^{4} fg\mathrm{d}x

    I understand how to deal with inner products, but I don't know how to find what the space orthogonal to the space spanned is. Any information will be appreciated.
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  2. #2
    Senior Member Tinyboss's Avatar
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    You're looking for vectors whose inner product with any vector in the spanned space is zero.
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  3. #3
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    "The space orthogonal to the space spanned by \{x^3, x+ 1\}" in what vector space? The space of all continuous functions? The space of all polynomials? The space of all polynomials of degree three or less?
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  4. #4
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    Quote Originally Posted by HallsofIvy View Post
    "The space orthogonal to the space spanned by \{x^3, x+ 1\}" in what vector space? The space of all continuous functions? The space of all polynomials? The space of all polynomials of degree three or less?
    The space of all polynomials of degree three or less.
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