Results 1 to 10 of 10

Math Help - Matrix Transformations

  1. #1
    Newbie
    Joined
    Jul 2010
    Posts
    6

    Matrix Transformations

    Hello everyone
    can anybody tell me if there exists any transformation between matrix addition to matrix multiplication (in any domain)e.g an addition in one domain for fourier is multiplication in the other. ??? i actually want to multiply a random matrix instead of adding it in my equation. what changes/effects do i have to make?
    regards
    aliya
    Last edited by aliyamazhar; July 19th 2010 at 12:59 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    Well, one option would be exponentiation. You can exponentiate diagonalizable matrices in a rather straight-forward manner: if A=PDP^{-1}, where D is diagonal, then e^{A}=Pe^{D}P^{-1}, and e^{D} you can compute by simply exponentiating each number on the main diagonal. Because matrix multiplication is not, in general, commutative, you might also need to have some condition on the commutator in order actually to set e^{A+B}=e^{A}e^{B}.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2010
    Posts
    6

    thanx

    Thankyou ackbeet for your reply. It indeed was useful to some extent. But it can make my solution complex as this method requires three assumptions:
    1. matrix A and B be commutive
    2. matrix A be diagonizable
    3. matrix B be nilpotent

    is there any solution which is more general than this? (i.e., without assumptions)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    Well, taking a step back, what's preventing you from simply multiplying in your equation? Multiplication is not commutative, it is true. So you do have to be careful. But if you have control over the way your equations look, then it seems to me you can just change to multiplication by fiat. I guess what I'm getting at is that a little more context of the problem would be helpful.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jul 2010
    Posts
    6
    Thankyou ackbeet . I think i am much clear on this now.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    You're welcome. Good luck!
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Jul 2010
    Posts
    6
    Hello,
    i need a bit more help please. with what factor is e^A.e^B is different from A.B? does any close approximation exist?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    I'm not sure what you're asking. Can you provide more context?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Jul 2010
    Posts
    6
    suppose two matrices A and B. Now simple matrix multiplication (i.e., A.B) is not equal to multiplication of exponent of matrices (i.e., e^A.e^B). right?
    i was just curious if these two multiplications have any relationship. ? for example does there any quantity 'X' exist for which i can say A.B=X(e^A.e^B)? or vice versa.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    I'm not aware of any X that will do that for you. On the RHS of that equation, you have two infinite series being multiplied together. On the LHS, you have simple matrix multiplication. There might conceivably be some sort of operation you could do, something like Fourier analysis, on the RHS in order to get you the LHS. But Fourier analysis on matrices is not something I've even seen. There is such a thing as the Fourier matrix (you can google it), but I've never studied it. I think you've definitely reached the end of my knowledge here, I'm afraid.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Matrix Transformations
    Posted in the Algebra Forum
    Replies: 3
    Last Post: February 18th 2011, 07:20 PM
  2. Matrix transformations
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: February 5th 2011, 07:59 AM
  3. Matrix transformations
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: October 28th 2009, 06:00 PM
  4. Matrix Transformations
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: November 18th 2008, 04:27 PM
  5. Matrix Transformations Help
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: July 7th 2008, 08:32 AM

Search Tags


/mathhelpforum @mathhelpforum