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Sudhanshu Ranjan posted an Question
September 01, 2020 • 06:42 am 30 points
  • CSIR NET
  • Mathematical Sciences

Is orthogonal complement of a subspace w of v unique?

Is orthogonal complement of a subspace W of V Unique?

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    Satpal singh

    https://math.stackexchange.com/questions/1106649/a-proof-that-orthogonal-complement-is-unique

  • Shashi ranjan sinha Best Answer

    suppose A and B be the orthogonal complement of W. Let x be arbitrary vector in A. Then, x belongs to V such that = 0, for all y in W. This by definition of B gives that x belongs to B. Hence, A is subset of B. similarly, we can show that B is subset of A. Hence, A=B so that orthogonal complements are unique

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