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Thread: Integration of Matricies?

  1. #1 Integration of Matricies? 
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    I'm computing this integral

    Int(exp(At)*B*BT*exp(AT*t))

    Where A is a nxn matrix
    B is a n x 1 vector
    BT = transpose(B)
    AT = transpose(A)

    If you could factor out the B*BT as a constant then you might be able to write it as

    B*BT* integral(exp(A + AT)*t))

    I can integrate that rather easily.

    I don't think you can factor B*BT out however. (since the order of matrix multiplication usually matters.)

    There are no integral tables for things like this.

    Anyways just looking for any thoughts or help.


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  3. #2  
    Forum Professor wallaby's Avatar
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    Well this is the first time i've ever heard mention of integrating matrices, so i won't be much help, but doing some matrix multiplication got me this.


    If the entries of 'A' and 'B' contain no dependence on 't' then the integral is made really simple, but i'm guessing this isn't the case in general?


    Last edited by wallaby; October 4th, 2011 at 04:53 PM. Reason: to correct wrongness
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  4. #3  
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    I found a way to integrate numerically in matlab finally. I'll plug this in later and see if I get the same results. It looks like you used the definition of exponential function as a series to simplify it a bit.
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  5. #4  
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    Quote Originally Posted by GenerationE View Post
    I found a way to integrate numerically in matlab finally. I'll plug this in later and see if I get the same results. It looks like you used the definition of exponential function as a series to simplify it a bit.
    That is what i did, although if you're using matlab then there's no point simplifying it... unless your matrix is very large, then the fact that is symmetric will help to (almost) halve the number of operations.
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