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Sudhanshu Ranjan posted an Question
August 24, 2020 • 04:28 am 30 points
  • 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

    Here I used the vector space V to be general , which may be finite or infinite dimensional. For Hamel basis, see this

    cropped2339836323286310934.jpg
  • Shashi ranjan sinha Best Answer

    No...see the attachment for infinite dimensional space

    cropped181804144505195631.jpg
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    but Hamel basis is used for infinite dimensional space. What if V is finite diminesional?

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    Yes I updated my answer by adding to it the term infinite dimension. I am giving you the proof for finite dimensional case.

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