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Quotient Space Linear Operator

  1. Aug 6, 2014 #1
    Could anyone help me solve this problem?

    Let A,B be two subspace of V, a \in A, b \in B. Show that the following operation is linear and bijective:

    [itex](A + B)/B → A/(A \cap B): a + b + B → a + A \cap B[/itex]

    I really couldn't understand how the oparation itself works, i.e, what F(v) really is in this problem.
     
  2. jcsd
  3. Aug 7, 2014 #2

    mathwonk

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    write v as a+b, then F(v) = a. now chck this is well defined, i.e. if a+b ≈ a'+b' modb, then a ≈ a' mod (AmeetB).
     
  4. Aug 7, 2014 #3
    I just have to ignore the sets that are in the operation? (v = a + b + B)

    edited:
    Just realized the definition of quocient space. Tahnks for helping
     
    Last edited: Aug 7, 2014
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