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Math Help - matrix theory ( ask about proofing the projection.)

  1. #1
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    Talking matrix theory ( ask about proofing the projection.)

    Let u be a non-zero vector of an n-dimensional Euclidean space U where n>=2.
    show that there exists a basis {y_1,...., y_n} of U such that the projection of y_i on <u> is 2u for i=1,...,n.

    thanks first
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  2. #2
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    Quote Originally Posted by lekge View Post
    Let u be a non-zero vector of an n-dimensional Euclidean space U where n>=2.
    show that there exists a basis {y_1,...., y_n} of U such that the projection of y_i on <u> is 2u for i=1,...,n.

    thanks first
    Choose a basis (e_1,\ldots,e_{n-1}) of the orthogonal complement of \langle u\rangle, define (y_1,\ldots,y_n)=(2u,e_1+2u,\ldots,e_{n-1}+2u), and check that it works. You did not ask for an orthogonal basis, did you?
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  3. #3
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    ya, i didn't ask about the basis, thanks for your answer.
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