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Sudhanshu Ranjan posted an Question
September 01, 2020 • 06:34 am 30 points
  • CSIR NET
  • Mathematical Sciences

Do there exists an orthogonal projection of a vector space v on an infinite dimensional vector subspace of v

Do there exists an orthogonal projection of a vector space V on an infinite dimensional vector subspace of V

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  • Shashi ranjan sinha Best Answer

    Suppose V is infinite diminesional vector space and W is it's finite diminesional subspace. Then, there always exist the orthogonal projection of V on W, say E. Then I - E is orthogonal projection of V on orthogonal complement of W, say U and V is direct sum of W and U. this gives you that U is infinite diminesional. Hence, you have an orthogonal p rojection I - E of V on infinite dimensional subspace U of V

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