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Math Help - Alternate Formula for Matrix Exponential

  1. #1
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    Alternate Formula for Matrix Exponential

    Trying to solve a proof for Linear Algebra:

    for a in the set of complex numbers, e^a = lim k-> ∞ (1 + a/k)^k

    Establish the matrix analog for any A in the set of real nxn square matrices

    e^A = lim k->∞ (I + A/k)^k

    I started off by trying the following:

    A = P D P^-1

    A^k = P D^k P^-1

    e^At = P e^D^kt P^-1

    not sure where to go from here or if this is the right thought process, I would appreciate any help I can get!

    Thanks
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  2. #2
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    Here is a link which better describes what I am trying to prove:

    The Matrix Exponential as a Limit of Powers

    if anyone could help me get further I would really appreciate it!
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  3. #3
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    Quote Originally Posted by Demagodnewb View Post
    Trying to solve a proof for Linear Algebra:

    for a in the set of complex numbers, e^a = lim k-> ∞ (1 + a/k)^k

    Establish the matrix analog for any A in the set of real nxn square matrices

    e^A = lim k->∞ (I + A/k)^k

    I started off by trying the following:

    A = P D P^-1
    You appear to be assuming here that A is "diagonalizable" which you are not given.

    A^k = P D^k P^-1

    e^At = P e^D^kt P^-1

    not sure where to go from here or if this is the right thought process, I would appreciate any help I can get!

    Thanks
    Follow Math Help Forum on Facebook and Google+

  4. #4
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    Shoot forgot to write that down. Sorry the problem does hint to solve by diagonalize, and that the matrix can be assumed to be diagonalizeable

    Thanks
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