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Homework Help: Linear Operators

  1. Jul 4, 2005 #1
    I'm not sure where to start with these proofs. Any suggestions getting started would be appreciated.

    1. Show that is A,B are linear operators on a complex vector space V, then their product (or composite) C := AB is also a linear operator on V.

    2. Prove the following commutator relationships for Linear Operators A,B,C:
    a. [A,B + C] = [A,B] + [A,C]
    b. [A,B] = -[B,A]
    c. [A,BC] = B[A,C] + [A,B]C
    d. [AB,C] = A[B,C] + [A,C]B
     
  2. jcsd
  3. Jul 4, 2005 #2

    Hurkyl

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    Definitions.
     
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