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Math Help - gram-schmidt procedure

  1. #1
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    gram-schmidt procedure

    I could use some help with the following...

    On P_{2}(R), consider the inner product given by <p,q>=\int_0^1 p(x)q(x) dx. Apply the Gram-Schmidt procedure to the basis (1,x,x^2) to produce an orthonormal basis of P_{2}(R).
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  2. #2
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    Quote Originally Posted by zebra2147 View Post
    I could use some help with the following...

    On P_{2}(R), consider the inner product given by <p,q>=\int_0^1 p(x)q(x) dx. Apply the Gram-Schmidt procedure to the basis (1,x,x^2) to produce an orthonormal basis of P_{2}(R).
    Okay, well, what do you understand as the"Gram-Schmidt procedure"? To start with you will want unit vectors. What is the length of the vector "1"? What is the inner product of "1" and "x"?
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  3. #3
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    Well, the way I understand it is that we are trying to find an orthonormal list of vectors in V. Here is the procedure that I believe is accurate...
    e_1=v_1/||v_1||
    e_2=v_{2}-<v_{2},e_{1}>e_{1} where <v_2,e_1>e_1 is the projection of v_2 onto e_1. This process continues for all e_j.
    The length of vector 1 is 1.
    And the inner product of 1 and x is just x I believe.
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