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Math Help - Minimizing Vector

  1. #1
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    Minimizing Vector

    Dear Colleagues:

    Could you please help me in solving the following problem:
    Show that the subset M=\{y=(\eta _{j})|\sum \eta _{j}=1 \} of complex space C^{n} is complete and convex. Find the vector of minimum norm in M.


    Regards,

    Raed.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by raed View Post
    Dear Colleagues:

    Could you please help me in solving the following problem:
    Show that the subset M=\{y=(\eta _{j})|\sum \eta _{j}=1 \} of complex space C^{n} is complete and convex. Find the vector of minimum norm in M.


    Regards,

    Raed.
    It's complete because it's clearly closed and closed subspaces of complete spaces are complete...for convexity I think you may be thinking too hard.
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  3. #3
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    Thank you very much for your reply. But what about the vector of minimum norm.
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  4. #4
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    Quote Originally Posted by raed View Post
    Thank you very much for your reply. But what about the vector of minimum norm.
    What about it??

    You need to show some effort. What attempt have you made in getting an answer?
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