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Math Help - Ordinary Differential Equation Problem

  1. #1
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    Ordinary Differential Equation Problem

    Show that if Y (t); an n by n matrix, is the unique maximal solution of the
    matrix IVP
    Y'(t) = A*Y(t); Y (0) = I;
    then Y has the characteristic property of exponentials, namely
    Y (s + t) = Y (s)Y (t) for all s; t E(element of) R.
    and
    Y (-t) = Y(t)^-1
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  2. #2
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    One way would be to use the fact that Y(t) = e^{At}, where e^{At} is defined as the sum of the series \sum_{n=0}^\infty \frac{A^nt^n}{n!} (of course, you have to show that the series converges in some suitable sense). Then the same proof which shows that e^{s+t} = e^se^t can be used in this context.
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