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Matrix Transformation

  1. Aug 8, 2010 #1
    Suppose two matrices A and B . i want to transform matrix addition to matrix multiplication. e.g A+B into A.B.
    Can anybody please tell me of any way i can do it ,except exponentiation? exponentiation gives an infinite answer.
     
  2. jcsd
  3. Aug 8, 2010 #2

    HallsofIvy

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    It is certainly true that [itex]e^{A+ B}= e^Ae^B[/itex] but what do you mean by "exponentiation gives an infinite answer"?
     
  4. Aug 8, 2010 #3
    [itex]e^{A+ B}= e^Ae^B[/itex] if and only if [itex]AB = BA[/itex]
     
  5. Aug 8, 2010 #4
    Don't A and B also need to be n x n matices?
     
    Last edited: Aug 8, 2010
  6. Aug 9, 2010 #5
    Thankyou all for your replies.
    "By exponentiation gives an infinite answer" i meant that suppose two matrices A and B, their multiplication A.B gives a finite answer i.e another finite matrix. but e^A.e^B give an infinite answer. doesn't it? Also can you please tell if there exists any X such that A.B=X(e^A.e^B)?
     
  7. Aug 9, 2010 #6

    HallsofIvy

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    No, it doesn't. If A and B are n by n matrices, then so are [itex]e^A[/itex], [itex]e^B[/itex], and [itex]e^Ae^B[/itex].

     
  8. Aug 9, 2010 #7
    ok thanx but " can you please tell if there exists any X such that A.B=X(e^A.e^B)?"
     
  9. Aug 10, 2010 #8

    HallsofIvy

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    ?? Of course their is:
    [tex]X= ABe^{-(A+ B)}[/tex]
     
  10. Aug 10, 2010 #9
    I think he is trying to come up with a logarithm function. But that would be quite restrictive since the function wouldn't be distributive in general.
     
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