Answers for Assigned Problems

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Assignment 6:

1. [A, B] = 

         (  9       3 )
         ( 6+2i    -9 )

      A* = 
        ( 0    3 )
        ( 2i   2 )

      Ah.c. = 
        ( 0   -2i )
        ( 3    2  )

      Tr(B) = 3
      det (B) = 2
      B-1 = 
       (  1   0  )
       (-3/2 1/2 )

      A does have an inverse.

2. A a = 

      ( 6 )
      ( 8 )

      ah.c. b = 2 + 2i
      atr B b = 8 - 4i
      a bh.c. = 
      ( -2 + 2i   0 )
      (  2 + 2i   0 )

     

3. Mostly proofs. Show that the product of two Hermitian matrices is Hermitian if the matrices commute. The sum of unitary matrices is not unitary, but the sum of Hermitian matrices is Hermitian.

Last revised 2005/083/16