Suppose e₁,e2, ..., en is an orthonormal basis of V and 0₁, 02, ..., Un are for each j. Prove that V₁, V2,..., Un is a vectors

Question

Suppose e₁,e2, ..., en is an orthonormal basis of V and 0₁, 02, ..., Un are for each j. Prove that V₁, V2,..., Un is a vectors in V such that ||e, - vj|| < 1/ √n basis of V.

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