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Sudhanshu ranjan Asked a Question
August 23, 2020 10:58 pmpts 30 pts
  • CSIR NET
  • Mathematical Sciences

Can a nonzero vector of a vector space v have zero image under every linear functional on v?

Can a nonzero vector of a vector space V have zero image under every linear functional on V?
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  • Shashi ranjan sinha thankyou
    See the attachment for finite dimensional case
    • cropped7936469461117266612.jpg
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  • Shashi ranjan sinha
    Here I used the vector space V to be general , which may be finite or infinite dimensional. For Hamel basis, see this
    • cropped2339836323286310934.jpg
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  • Shashi ranjan sinha Best Answer
    No...see the attachment for infinite dimensional space
    • cropped181804144505195631.jpg
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    Sudhanshu ranjan
    but Hamel basis is used for infinite dimensional space. What if V is finite diminesional?