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Math Help - How to construct a perpendicular vector w.r.t a bunch of known vectors??

  1. #1
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    How to construct a perpendicular vector w.r.t a bunch of known vectors??

    Hi,

    Given several vectors, which may be or not be orthogonal to each other, how to construct a vector perpendicular to them? In a sense of inner production being zero.

    To be specific, I have n vectors v_{N} of length N, where n<N. So the maximum rank for these vectors is n, which leaves space for new vectors perpendicular to all of them. How to construct such a vector? I know Gram-Schmidt process, but it seems it's not what I want.

    Thanks.
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  2. #2
    Super Member Rebesques's Avatar
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    Re: How to construct a perpendicular vector w.r.t a bunch of known vectors??

    I doubt whether any other process can make a more effective use of Hilbert space structure.
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