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Dual space bijection

  1. Oct 27, 2012 #1
    1. The problem statement, all variables and given/known data
    let V be finite -dimentional and T:V->V*(V* is the dual space of V with same dimension as V) ,let ei be the bases of V,e^i be the bases of V*,consider the linear bijection :K:V->V* defined K(ei)=e^i,show that this bijection depends on the original choice of basis.

    2. The attempt at a solution
    choose ei to be the bases first,then prove K under this bases is bijetion.then choose ei' to be the bases, and then prove K under the new bases is bijection , is my proof right or wrong???
     
  2. jcsd
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